I don't think that's actually what the FAA has reasoned.

FAA calls all of these devices, in general, child restraint systems. Rigid seats with harnesses are allowed under FAA rules. The real consideration is blocked egress, since a large, rigid device strapped to a seat could actually make egress more challenging. That is covered in a more subjective advisory circular, which allows airlines to make policy, e.g., it may only be used at a window seat of a non-exit row.

Since FAA just this month has decided to start enforcing a 1992 rule requiring even so much as a paper cup to be stowed before pushback citing the egress concern, we might even expect some new policy on this.