They are single use items in terms of crash protection. When you see car seats after a crash test sometimes they're damaged (plastic stress, cracking, bent parts) even though they have protected the crash test dummy well. A lot of modern car seats also have stuff like EPS foam which will compress to hopefully absorb some of the force away from the child, then it's useless if it's already been compressed. I think this probably only happens if there's a child in the seat, but the advice to replace applies whether it was occupied or not. I guess because depending on the severity of the accident, the seat will get jerked around and potentially impact off the side door etc.
It's a precaution rather than a definitely studied thing, but for sure if you've been in a big impact (ie, hit something human sized or larger at speed, anything causing more than superficial damage to the car) it is usually trivial to replace seats since insurance covers it, and the thinking is better safe than sorry.
It's the same thing with bike helmets - you wouldn't have a nasty crash and then keep using the helmet. Buy a new one.
And seatbelts - they stretch and warp if they have been in use at the time of a serious collision, and if the car is not written off they may need to be replaced, even if the occupant was not seriously injured.
(Pheasant probably doesn't require replacement of the seat.)