I do recognise that a lot of it is probably just playing up for the joke, but I assume it has to come from somewhere. I regularly see posts where basically Person A sends an odd image/message, then follows up with "wrong number, sorry" and Person B responds with "wait stay".
Do Americans, as a rule, not save phone numbers? Or is it purely a bit that has become a trope?
It's not a specific US thing and it happens because people save the numbers.
It's less likely that someone types in a wrong number these days, but wrong number calls/messages still happen when a number is reused.
It's good practice for operators to allow a period in-between reuse, but it can still happen between people who don't get in touch very often.
Also, prepaid simcards reuse the same numbers very quickly, because the operator only reserve about as many numbers as they need.
So if you've stored the number from someone using a temporary prepaid simcard, it might very well be someone else on that number whenever you try to call them back just a month later.
In Australia when you register a simcard you have to provide a drivers licence. As I understand it in the US you can just buy a simcard thats valid for X days or X call value whichever comes first. No ID required.
Oh holy shit this makes so much sense... I'm also Australian and I've always wondered how a prepaid sim would help drug dealers in TV shows and movies and such because I just never thought that requiring ID to activate any sim card might not be a thing elsewhere