Your logic makes sense. To OP’s point, though, you wear an engagement ring to show that you are engaged; a wedding ring to display you are married/wed. The argument for it being called when you receive it is weakened by the fact that most people remove their rings when an engagement is broken, or they get divorced. Or, they move the ring to a different finger, at which point it’s no longer an engagement or wedding ring, right? It’s just a ring.
If the rings were named after the event of reception, they’d still be called wedding and engagement rings even after a broken relationship. They’re “was” rings; ex-wedding-rings. No longer engagement rings.
So the more I think about it, the more I’m with OP - the rings represent a state, and so wedding rings should be called “marriage” rings to represent the state of being engaged/married, rather than the singular event of the giving.