saved $159 by canceling on booking and rebooking with the hotel

It’s typically cheaper to book direct. Many hotel websites even display this - “Book on our website and save xx%”. It is often easier/safer to make changes when you book direct. The establishment likely pays a fee to booking.com each time a room is booked. They avoid this fee otherwise.
Those of us who watch our $$$ try to cut out the middleman whenever we can.
You will find many posts on this forum about using booking.com as a means of getting some suggestions as to the lodging you want, options, etc. It is a great site for that. BUT you will find that there are many posts stating that you should book direct.

Excellent discovery! I always try to book directly with the hotel but I always check on Booking.com. I like their reviews and I like that they always offer the square footage of each room, which is important to me.

While I'm on Booking.com, I will check the price vs. the hotel price. Usually they are similar. But sometimes Booking.com is less expensive and so in those cases, I will book there, as long as it is a refundable reservation.

Different strokes for different folks. For some people the hunt is part of the fun, for others it is a major hassle. Using a third party website that provides free cancellation up until several days before arrival seems to me to be a form of "travel insurance." My experience with trying to cancel directly with a hotel a few days out is not recent ... but I recall it was complicated. If your dates and locations are firm then contacting the hotel directly if it saves money seems to be a no-brainer. Having said that I always start with booking.com and pick a likely area and a reasonable hotel price and then ask the website to show that hotel on the map. The costs of all of the other hotels in the area will also be shown, which is good information to have whether I book through the website or directly. And you can pick different areas to compare prices among areas.

I always book direct with the hotel, not so much for the price, but because I don't want to have a third party to deal with in case of problems or changes. For holiday travel, my plans are usually firm. For business travel, I just pick a rate that allows late changes and payment on arrival, and I've never had a problem making them. No reason why this should be more difficult doing this with a hotel than a third party booking site.

I have been successful in 20 years of travel to book wherever I found the cheapest price online.

Sometimes the price is more on the hotels site sometimes it is less on Booking.com and vice versa.

Realize that many small mom pop owned hotels compared to big chains do not have money to pay a webmaster or websites of their own compared to the big chains so they pay for a listing on a successful aggregator like Booking.com that is available in multiple user languages. They also get more exposure that way by showing up in the listings where I can filter the search results by price and rating's.

I typically use Booking.com for my searches and also my reservations. Right now I have 21 reservations on Booking.com for two international trips next year. I move frequently during trips and having everything in one website location makes it much easier for me to find my reservation. I’m able to consolidate everything while making sure I don’t have a gap night without lodging.

I do look at a hotel website when I will be spending more than three nights there. For instance, I will be in Palermo, Sicily for five nights, so I booked that reservation directly with the B&B.

For the most part, I use booking to do research as well as book. With booking, I book early but keep my eye on the prize and very often will find a better deal before my travels. Cancellation has always been so easy on booking. There has never been a problem.

But I sometimes book directly on the lodging website.

Last time I went to Seattle, I had booked a Marriott through booking. I am a member of Marriott rewards and also a senior citizen. I decided to check out how much it would be if I booked directly on the Marriott site. I was shocked when i found out that i was able to save over $100 by booking directly with Marriott. And that is what I did. I canceled my reservation with booking and booked with the Marriott for over $100 less.

I trust booking and feel safe and protected by them.

I usually book by booking.com. I check prices along the way on what I have booked. Sometimes the price goes down. So I cancel and rebook.
People who call hotels, I don’t know about that. Especially to overseas. The thing is you do not know you are getting a better price unless you also check the booking engines. So comparisons are in order to do that. When you call overseas to a hotel you have to figure the time difference and hope that the person on the other end has the authority to make a price change and that that person is there at the time you call.
It seems that the penchant to call a hotel is motivated more by the thought that you want to help the little guy instead of getting a better price. And by an aversion to the “big guys”. In the same way people hate Walmart. However, the little guy may not even get as much business without a booking service verses direct contact with the hotel and perhaps no way to even know there is a hotel/lodging without it being seen on the internet.
Used to be I would show up in a town and go door to door asking about rates. That limited me to actually seeing the hotels visually. I might never know about the one around the corner and off the main area.
A site like booking.com services all those concerns. And even services those who do book direct because all the info is there for you to seek places and reviews and prices. So the direct bookers need it too.

I have, more than once, sat in the lobby of a hotel and booked a room or an extension of nights on booking.com because it was cheaper than the hotel rate. Even this after speaking to the front desk, in person, showing them the booking.com rate and asking if they could do better. No, they could or would not beat that price and I should go and book it on booking.com.

I definitely pays to check every avenue. I mostly use booking.com for trips, but do really pay attention to make. sure I am comparing the exact rooms and whether breakfast is included. That can change the price dramatically.

For an upcoming trip, I booked a hotel on booking and then we decided to change the hotel. I looked at both their website and booking and while we were comparing the two, my daughter looked them up on instagram and they had a promo for breakfast, which normally would be 27 euro per person. We are staying there for a week, so it definitely paid off.

So far, I have never had an issue using booking, even twice when the hotels were nonrefundable. One time booking sent a note and suggested contacting the hotel as they may refund, and they did. The second time I just called the hotel and asked, and they did. Both of these were within the past year.

jazz+Travel is correct. Many small b&b’s don’t have a website so they need a sight like booking.com. You’ll find this up and down the coast of Croatia and on some of the islands. Our cousin on the island of Korčula uses booking.com because they only have 4 rooms to rent. They also live in the house.
I will also research on booking.com and look at reviews, location, amenities (elevator, a/c, laundry, etc). I have found places we like, I put in their name on a search engine, and it will sometimes come up to book on booking.com.

I'm traveling now, staying in my Booking.com hotels. A feature I appreciate is choosing the option to not pay in advance, not even a deposit almost all the time. (You have to be careful, since the cheapest option will likely be paying up front and non-refundable.)
Because I plan so many months in advance, for my budget it really helps to not have to pay until the travel is actually underway. I also appreciate how easy it is to cancel or make changes with their system.
That said, I always then email or call the hotel directly to make sure my reservation is in their system, and a query about check in times just to check responsiveness.

Also for correspondence, I have had excellent response from the places I reserve on Booking.com. I almost always am staying in small hotels or B&B’s. When I make a reservation, I will write a few sentences greeting to them and tell them I’m arriving by train from “x” town (no car parking needed). Often I receive a nice comment back, and it’s within 24 hours.

Would you say that I have just been naively making a mistake not using google maps and/or booking to discover logging places but then trying to reserve directly with the hotels?

Not at all. There are times when booking sites offer lower rates, and you may have benefited from that. There are times when it's less expensive to book directly with the hotel, and you obviously have benefited from that with the hotel in Key West.

Bottom line, there are pros and cons to each way. Cancellation terms and policies may be different, and the rates may be different. There is no right or wrong way -- just preference.

I prefer to book directly with the hotel. It eliminates the middleman, and I just prefer to deal directly in case anything needs to be adjusted. But then, I'm old school. Others feel differently, and that's ok. Just research well and do what makes you comfortable.

Sometimes on Booking.com you see a hotels that has a few rooms listed, and a few prices, the cheapest non-refundable, then a rate that lets you cancel before a certain time before you chosen arrival date, then maybe higher prices for rooms with more amenities, more beds, and so on. ... by accident I got up to "genius level 3" on booking, which might save me some small amount on the rooms on the site that specify "genius discount". If somehow I loose my written itinerary for my next trip and I made reservations on a site like booking, and if I forgot which rooms I reserved, I guess I could log into my account on booking and look up where i am staying.

With regard to losing paper itenerary with reservation information, consider what we do -- if you've not thought of doing it already. We have written confirmation sent to us via email and we print that out and take it with us. If that is lost, we can always access our emails showing the reservations our phones.