Let me preface this by saying that at the end of this message I can give you a little more anecdotal information but I'm going to start with some of the industry info: Much of the physics behind the art of luthierie is unquantified. It is just there and we either apprehend it or ignore it. Yes, the original intent in creating the solid body electric guitar was to minimize vibrational effect, but:
1) You'll notice that the original poster didn't limit this to solid bodies only
2) After sixty years, the very personal build signatures of the various manufacturers either remain or have been returned to. What was discovered was that the original intent (minimizing resonance) failed and the manner in which it failed was part of the signature sound of the instrument. As a result, the classic guitar designs retain some of their basic sounds whether or not you swap in various types of pickups. A Strat with humbuckers still sounds like a Strat with humbuckers rather than a Les Paul. A Les Paul with single coils (such as the P-90s) sounds like a Les Paul with single coils. In fact, the classic manufacturers are haunted today by their own designs and by enthusiasts who want the sounds that those guitars made. Some of the differences they are chasing are differences that make a difference and some aren't, but everyone agrees that those who have returned to the original designs have recaptured a different sound.
3) There were attempts to either make the classic designs easier to build or better in the '60s and '70s that caused the guitars to sound...
different. The biggest changes were in bodies, necks, and neck joints. In this period, Gibson in particular pursued massiveness and rigidity in order to further pursue that goal you spoke of and in order to increase sustain. They accomplished their goals but the guitars sounded quite different, and some people didn't like the change. If you want a "sweet" Les Paul, the '70s era might not be the easiest to find one from. However, if you want a
powerful one, the '70s is your period. Younger players are flocking to them right now. Interestingly, the "T-top" pickups from the early '70s are very much appreciated by the Les Paul community (including the old-timers) as reasonably close to their earlier cousins while the bodies and necks are much more controversial.
I, for one, came across most of this information anecdotally and through study. For instance, my first really good electric guitar was a '74 Gibson Les Paul Standard I bought used in '78. I spent years wondering why it didn't sound like some of the classic guitars from the '50s that others had. Then I discovered that there were build differences. I now own three LPs, each of which has its own character - the '70s LP, powerful with endless sustain, a 2007 that is
far sweeter and airier, and a 2011 LP with P-90s that has a much brighter sound but still has the compression and chunkiness of the mahogany body/maple cap LP body. I've played the all-mahogany LP juniors and specials with the same pickups and noticed that they sounded MUCH thinner than the LP with the maple cap.
I also needed a Strat for my work in sessions so my lovely wife had one built up with a rosewood fingerboard because I didn't like the polished maple ones. I spec'd a swamp ash body to give it the brightness of the maple neck. However, after trying for a good while to get a certain spanky sound out of it (look at 2:17 on
THIS video) I discovered that the way to get that sound was with an alder body and a maple neck. (I sure wish YouTube videos were available back in the '70s.) With alder/maple, it just falls right out.
Now, notice that most of the sounds I was searching for in these examples were low-gain sounds. Yes, you can gain up to the point where there is less difference between the guitars. But that isn't the range of sounds I'm going for.
Bob