Hmm, sounds reasonable. A firm rubber should be able to deliver even pressure, without smooshing between the leads. And even if the plating (of board and lead) aren't very friendly, this pressure can be increased almost arbitrarily (using ever-higher durometer push-pads, up to the limit of PCB, or even lead deformation -- this could get very tense indeed with a ceramic PCB and carefully fitted clamps!). Yeah, you'll want a bracket under the footprint to support this clamping force, and hard gold is probably the best plating option, even if not ideal against the most common (tin) plating used on components.
The sheer area taken up by the clamp, and the amount of deformation used, may again limit performance though. You can't place components there. You might not even be able to place vias there: the compression and squishing of the PCB itself may fatigue and crack them. Ditto for ceramic chip passives.
If vias are reliable, you do at least get the benefit that a multilayer board can be used, immediately underneath the footprint; you eliminate the long looping connections of a spring type socket, giving good GND/VCC at least, if not as great GPIO signal quality. Planes provide good bypass, without having to rely on chip caps placed right beside or under the part. (Ah, assuming you don't mind that the socket is customized to each particular device it's being used on..!) And signal quality can be dealt with, to some extent, at modest distances from the pins; give or take what kind of device we're talking here. (A cm or two stub length is perfectly fine for an MCU, and probably fine for a typical LVDS rx/tx pair, but wouldn't be so great for modern DDR, or PCIe and other high speed differential channels, or precision RF circuitry.)
Probably, much less clamping force is necessary than where all these various mechanical limits manifest at, and it'll be reliable after all, or at least useful (hundreds of cycles, maybe thousands?).
These are somewhat unusual questions to ask of a PCB, i.e., the particulars of strength, elasticity, deformation and fatigue -- so it would be nice to find some technical papers discussing them.
I wonder what kind of centering and latch mechanism would be best. Some kind of over-center clamp or cam would be typical I suppose. A chain of levers and right-angle links might be used to synchronize them. The clamps do need to move out of the way of the chip for insertion/removal, then something either sitting at the bottom (a plastic film cutout?) or grabbing the corners (but it has to move out of the way of the clamps..?) keeps it centered while unclamped. There might not be room to get tweezers down in there (reliably anyway, seeing as most parts have a tapered body making it difficult to lift from above the parting line), necessitating gravity (turn it upside down..) or suction to insert/remove parts.
Oh, also you could turn this kind of on its face. Going back to the spring style sockets, what if instead of a long loop, simple leaf springs are used? Probably a PITA to retain leaf springs of such fine pitch; but the loop area could at least be kept short, and the springs can simply slide in horizontally, lapping over the leads as they do (which also causes contact wiping, and pushes the part into the center -- if the slides are synchronized precisely enough, that is). The PCB footprint would simply be a regular TQFP with the pads pushed ponderously far from the body; the part itself rests on bare PCB and the springs bridge from the lead top surface to the nearby pads. Possibly, less clamping force would be needed (granted, a hundred springs working together is still quite a mechanical advantage), so that the mechanism can stand up from the board a bit perhaps, giving more clearance for nearby passives.
Tim