We fit three small kids in a 2004 Focus Wagon, but it was an exercise in finding the exact seats that would fit.
It has a lesser crash rating than modern cars, but the reason is there are structural elements that drivers legs could hit in a crash (https://www.euroncap.com/en/results/honda/cr-v/15568). Basically I thing the car is too stiff for Euroncap, but it does not make it less safe in my opinion. Crumple zones are sized for standardized impact tests.
Acoustic stuffing probably takes much space two.
And I agree for the pillars.
Airbags mostly take up what on other cars was dead space behind trim.
Crumple zones #1 function is to buy time for the airbags to deploy between when the front of the vehicle starts slowing in a crash and when the cabin starts slowing. Think about it, if the cabin decelerated at the same rate as the front bumper the occupant would be half way to the steering wheel by the time the bag finished exploding and they'd get hit in the face with an exploding airbag. Crumple zones #2 is deceleration and is tuned for a specific speed of impact. They can be thought of as a single use coil spring without a damper. Too slow of an impact and they do little to nothing (no big deal because it's a slow impact). Too fast and you will blow right through your available travel and bottom out hard. Because the car manufacturers are not staffed by idiots they respond to incentives and tune their crumple zones to be most effective at crash absorption at the high end of the speeds they are tested at.
Most of the increase in "wall thickness" so to speak, of vehicles is from pillars and body structure that increases in width (to get more strength without adding too much material and weight). Then the trim is layered over that and that means you not only lose the space where the reinforcements are but over the whole vehicle.
You see this with the ridiculously high belt lines that are "for safety" but have the convenient side effect of reducing the amount of glass.
No. They really don't. You can shove airbags in anywhere and the passenger cabin is not a crumple zone and is supposed to be rigid. The reduction in interior space comes from fatter structure in the pillars and the various other reinforcements (for that cabin rigidity). Then you add fatter interior trim (to hide fat wiring harnesses and reinforcements and thick sound deadening while still providing clean-ish lines) and the effect compounds.
(I buy the hypothesis. Just too much fun to not make that joke.)