I suspect that the less the structure housing a transducer moves/resonates during use.. the better it can sound.. or at least the less it would influence the sound (although this wouldn’t seem to be a linearly proportional relationship). It might have a negative effect if it’s within the operating range of a particular transducer. If the structure is perfectly motionless at any frequency or amplitude (regardless of what the transducers are up to), that would seem to be a perfect enclosure as a foundation for audio reproduction. No energy loss. Exhibit A.. Acora speakers. I think I remember one of the Acora’s (or a presenter?) saying the reason for the granite enclosures was so the kids or dog couldn’t knock the speaker over, but they were probably half joking.
If the footer technique merely transfers the resonance of the entire structure above or below the operating range of the tweeter/midrange, then that may be acceptable (much like we find second-order distortion acceptable with amplification in our electronics). Of course that assumes the entire structure is rigid.. if the panels or sub-components independently move to their own resonance frequencies.. then that is another problem and it’s unlikely what you place underneath will help as much as you hope.
I’d also suspect that a speaker with a large monopole woofer being driven by a high current amplifier (at high levels) and it’s cabinet is resting on ceramic balls or springs or any soft material with a range of motion.. that can’t be good for the impulse response or phase continuity of the other drivers. Coupling with a large mass might be a better solution (vs decoupling), if done well.
(Disclaimer: I’m not a materials specialist or a physicist.. just an audiophile who used to like physics once).