Dear Intact (Dave?)
I agree with your statement about logical structure. That's why I embarked on the project of acquiring the idler-drive and direct-drive turntables and then making slate plinths for them, so I could hear for myself in my own system. (I also bought a Garrard 301, but I realized along the way that I had no energy left to wade through the Garrard options, plus I grew to love the Lenco, so I re-sold the 301 with no plinth.) Little did I know it would take the better part of two years (of my "spare time") to identify and solve the problems associated with making the plinths that I did make. That's also why I don't feel qualified to make any broad generalizations, beyond slate is "good". Something else might be even better.
I neglected to mention that the Kenwood engineers apparently also valued the idea of Constrained Layer Damping and the use of disparate materials perhaps to spread out the resonances. The L07D plinth is primarily made of the very dense cement-like material described above (if you look at a photo of the L07D, the stuff I am talking about is painted dark bronze or brown and is the major visible structural element), but hidden below and around the motor/platter area we have a sheet of thick stainless steel or aluminum. Below that is a very large piece of intricately cut hardwood (mahogany maybe) which is bolted up to the bottom of the chassis by at least a dozen metric screws that anchor into the stainless steel pan. (The wood piece can be seen peaking out around the side edges of the plinth; it is painted light gray.) Finally, that stainless steel or aluminum piece that surrounds the motor gives off a solid metal "arm" that goes all the way to the tonearm mounting platform, forming a firm coupling between the bearing and tonearm bass, which also contains a very heavy brass anchor-weight. Those guys were not fooling around. When I first acquired the table I had the notion of replacing that hardwood piece with a piece of slate, but it would take both a waterjet AND a CNC machine to re-create the shape in slate, I will leave well enough alone.
Maybe the answer to the OP's question is that it takes a real knowledge of materials science and that possibly a variety of materials used together in a certain kind of "sandwich" would make the best plinth, cost no object.