Thought of that too, but considering the big place that Obadiah has in Tony's life since he was little now, Jarvis being there along too would be awkward. Thing about movie!Tony is that he's more damaged (maybe that's why I like movieverse Steve/Tony, Tony is extra woobie).

Like, if Jarvis was there all along, and he's a smart guy, why didn't he figure out Obadiah?

The complication can be solved with a simple flashback. Or that could be included as a backstory for people who bothered to look it up.

Mostly though, I'm just thinking of Fic Fodder to include Jarvis in the movieverse!