Although I know some hotels show a "rack" rate on their website that is higher than any booking website's rate, I don't go to those places. For all of the places I've looked at, rarely was the directly booked rate more than the booking website rate, and then it was by a negligible amount.
I'm sure that booking sites try to assure that the hotel will not offer a lower rate on their website, but there are a lot of ways for hotels to get around this. Often, the hotel will only offer on the booking website their most expensive rooms (say larger or with a balcony), but if you don't care about these things, you can find less expensive rooms by booking directly.
I once booked a five-night package deal in a lodge in the Harz that included halb pension (both dinner and breakfast) for the same rate as booking offered for a room with only breakfast. I estimate a saved 30% for those 5 days by not having to pay extra for dinner.
Three years ago I booked two nights in a hotel in a spa town in the Black Forest. I just now checked several dates for that property on Booking and got a price of €216 for a double room for two nights. Booking says some rooms have balconies. A double room with a balcony to two nights next month would cost €208 on the hotel's own website. I actually booked a package deal only available through the hotel for two nights with a variety of additional benefits around town for €198, today. I only used one benefit, free spa entrance for two, worth €39, so effectively my rooms was €159.
For that small town near Würzburg, the average price of a room booked through Booking would be €109,50. The average price booked directly with the same properties would be €99,67. Two were the same booked directly; four were less.