Like engagement rings denote the engagement… Maybe it’s just English being its usual mess
Yeah, you get it at the event.
OP is acting like a birthday gift is only a birthday gift on someone’s birthday…
Your logic is sound, but backwards.
Marriage is more analogous to a birthday. (A personal change in status)
Wedding is more analogous to a birthday party (i.e. the event celebrating the change in status).
As you pointed out in your logic, the birthday gift isn’t really about the birthday party, just like the ring doesn’t commemorate the wedding celebration, it commemorates your new marital status.
Unless of course you are the kind of person that is so focused on the wedding celebration that you forget the reason why you are celebrating to begin with (spoiler: you are making a commitment and entering a new life stage).
I think OP is on to something.