this would probably work and maybe even work great - but the issue is that it would be an all or nothing proposition - you would have to commit to the full system from the start, and then it would be very hard to transport to a new location …
whereas with randomly distributed subs you can start with one sub, then add another, and just keep adding them for as long as you like … you can move to another location - you can sell individual subs or you can buy second hand ones and not have to get anything custom …
basically with distributed subs the system grows with you as additional funds become available and / or as your demands for bass increase … and you can still tune out modes electronically because each subwoofer can also be run essentially as an active bass trap depending on what signal you send to it assuming each one is on a different amp channel and you have enough processing …
and as for 4 feet of foam i realize that was a joke but even million dollar studios can only afford 4 INCHES of foam - which is the thickest acoustical foam i have seen for sale.
acoustical foam is very expensive.
what you could do is put some resistive vents in the wall that vent to the rest of the house, for example you could cut round 4" holes in the drywall on front and back sides but have those holes deliberately misaligned so that air can’t take a straight path through, then stuff the space between front and rear drywall with polyfill to introduce some resistance - this would be more cost effective than acoustical foam but you would lose compression and thus ultimate room gain at very low frequencies …
acoustical foam is really meant for vocal range where thinner foam works and where any compromises to sound quality are not acceptable.
so yeah while your suggestion theoretically would work i think there is a reason why nobody is doing it - it is just too extreme.
even the pentagon has to work with budgets and often projects are cancelled because they get too expensive.
i am not against your idea - but i would personally not have the balls to attempt it.
i would be far more comfortable with something that will still work and be usable if it is only halfway finished.
and the final point i want to make is regarding efficiency.
although in open air a soundwave involves both compression and acceleration of air there may be circumstances where these two components aren’t exactly mirroring each other …
for example with microphones there is an effect where when you move the mic closer to your mouth it begins to sound more bassy ( called proximity effect )
in other words under some circumstances we have to change the way we think about sound …
in YOUR room for example you would be mostly using amplifier power to ACCELERATE the air rather than compress it … whereas in MY room i would be using amplifier power mostly to COMPRESS the air rather than accelerate it …
and just as the microphone has different behavior at high and low frequencies when placed close to the mouth i think our ears may have a different behavior at high and low frequencies when it comes to sensing air acceleration versus pressure …
that is to say at high frequencies probably our ears sense both but at low frequencies they probably only sense pressure …
so it is maybe more efficient to try to create pressure than acceleration if you want to hear and feel loud deep bass in a small room …
this is to some extent the same as saying that the rear array would be canceling the energy of the front thus wasting output … but of course because of standing waves it is not that simple …
in other words if cost is truly no object then your suggestion should work.
but i disagree with the characterization that it is a “simple” solution
( i realize you were part joking )