I dicked about with record/platter interfaces when I worked for Garrard.
It certainly made a difference to the cartridge output (we used to look at the cartridge output measurement as the principle indicator since if something did not cause a problem here it wasn't an actual problem for the playback).
A lot of people, including some engineers, use static thinking for dynamic subjects. This leads to wrong conclusions.
For example, who knows how a "crankshaft damper" works in an IC engine? Basically it isn't a damper at all it is a mode-shape changer. By attaching a torsional spring and rotational inertia to the crank tuned to the same frequency as the torsional mode to be changed what happens is that at the frequency at which the crank used to resonate the little flywheel is resonating on its rubber spring so the mode shape of that resonance has been changed such that even though there is something resonating away like mad it isn't felt by the engine/transmission/bodyshell/driver.
I found that things could resonate on a record player without giving any output to the cartridge, and sometimes simple solutions, like a carefully placed punched hole in the top plate, could stop a particular structural resonance getting to the arm base and hence to the headshell (of course the cartridge output doesn't know whether it is the stylus or its body that is vibrating - both give an output).
I digress, the difficulty with record clamps is one of basic production engineering. All the theory is pointless if you don't have a perfectly flat record - which you don't. Non-flat, ie all, records only touch the mat or platter at a few points so a clamp will vary in effectiveness from disc to disc.
My own record player has a -0.060" cone for a top platter surface such that the disc sits with only its periphery touching the platter when it is dropped on but when the clamp is applied the whole disc is in contact as long as any warps are less than 0.060 high.
There may be other well thought through record players or solid mats which do this but most don't and a weight or clamp is therefore of limited and varied efficacy. I don't bother with one with my other 3 record players.