It seems nobody knows why it started, but it seems pretty intuitive why it's continued -- it looks fancy and formal and important. You went to the Cinema and you had an Experience and at the end it was capped off with a fancy set of Roman Numerals. It's silly like a hundred other aspects of the movies, but it's kind of lovable.
And I can't help but assume that fanciness derives from years being carved in stone as roman numerals for Important Things. On buildings (date of construction), memorials (for wars and important people), and of course gravestones.
I mean, it also wasn't Star Trek 3, it was Star Trek III. Because fancy.