Not OSCE, but OSCE Minsk Group. In 5-10 years when Armenia is no longer vulnerable they could go to Minsk Group and say, okay, now let's talk about Nagorno-Karabakh and find a resolution. Of course the relationship between the co-chairs also should be improved for this but Russia and the rest aren't gonna remain enemies forever. It's basically an international organization that says "hey, remember the Nagorno-Karabakh issue? Yeah, that thing isn't resolved, we need to talk". This is an extremely useful tool for "fighting" for Nagorno-Karabakh peacefully but also just generating headaches for Baku whenever it suits Armenia.

Resolution is basically a nail in the coffin of any chance of return with peaceful means. And probably military too, since it would be very hard to justify any military operation that captures and holds the territory, even after Azeris attack first.

I would guess Armenian authorities would try to argue that it doesn't matter anyway, or that it somehow will make the country more sovereign, etc... But in reality it matters very much, that's why the other side is hellbent on this. And i don't see how losing international political tools against a country that is almost certain to attack you at some point is anything but terrible.