What is that based on other than them wanting to sell more seats? I'd imagine the materials don't erode, otherwise how safe can it even be in the first place?

Nothing. It's a marketing gimmick to depress the used market. The only way they "expire" is if the regulations change, which does not happen often.

I thought that was an American thing since I couldn't find it on our car seat

So ours has a manufacture date and I know people look at it and if it's older than 3-4 years they won't buy it off you, but as far as I can see that advice isn't anywhere in the manual of the seat. Maybe some seats "expire" in some way, but it sounds like an urban myth.

Don't think it's an urban myth, this article shows a car seat with an expiry date next to the manufacture date.

https://psychoautos.com/why-does-my-car-seat-have-an-expirat...