Hi and a warm welcome to the forum gang, Janice!
I'll preface this by admitting I've never been on an RS tour but have been to Rome, Florence, Venice and the Amalfi Coast.
You have walking tours most mornings and the afternoons free, but that
puts other tours (Colosseum, Vatican, Doge Palace etc.) in the
afternoon when you are perhaps tired from the walking tours which they
keep mentioning are 2- 6/8 miles. I wish some of those must-see places
were still included in the trip and not on our own.
There are all sorts of reasons for this type of schedule but if I was to guess, some of the biggies, like the Vatican Museums, are so mobbed anymore that 1-2 people people can move more nimbly on their own than a guide can move a group. Depending on time of year, mornings are more comfortable, temperature-wise, than during the heat of afternoons, and streets may not be as crowded.
As suggested above, a great way to manage sightseeing at a slower pace is to arrive several days before the start of a tour, and stay several days after it wraps up. The 'Holy Trinity" cities, especially, are well used to hosting tourists from all over the world, and it would not be difficult to you to manage on your own.
I'll also go along with the advice to postpone the Amalfi Coast for another trip or another tour. As mentioned, it can be time-consuming to get to, time-consuming to get around, and can be very, very busy. Best to leave that one until after you've experienced a maiden voyage to the Boot?
Will we be overwhelmed and wish we had more smaller cities in the mix?
You might. It depends on your tolerance for busy places, and what you're willing to put up with to see/experience them. For instance, the Uffizi in Florence is a VERY busy museum but as an art geek, I wouldn't have missed it for the world. Also, with extra days you can visit some of the excellent smaller attractions that aren't as mobbed or have better crowd control, although sadly you couldn't do that with Florence on the VFR tour. As suggested, you might look at tours with a mix of bigger and smaller cities? You might also think about going in one of the winter months (spring and fall are no longer shoulder seasons, if there's even such a thing anymore.)
We all travel differently, and RS tours move at too rapid a pace for my husband and I thus we haven't taken one (yet). That said, per the reviews and posts above, they DO work very well for many! It's up to you to know your own travel style and determine how well you might enjoy them. Tips for booking tickets? The forums are full of 'em, plus we can cheerfully answer questions you might have about specific attractions, such as the official websites for ordering. :O)
Editing to add: The VFR tour is really closer to 8 days than 10 as it doesn't commence until late afternoon on Day 1 and is over at breakfast on Day 10. That may be a factor in deciding to add those extra days, if on the fence about that.