Private pilot here. Mechanical attitude indicators don't need to be reset on level ground, when they first start spinning they're almost always tilted but once they spin up they level out on their own. Because they're driven by vacuum from the engine, sometimes they don't fully spin up and level out until the engine's being run up or takeoff.
I've always wondered how the attitude indicator self levels, and the OP's explanation sounds plausible. Next time I go flying I'll have to spend a few minutes in a constant rate turn to see if I can make the attitude indicator drift like he says it should.
Edit to add, here's a link to a youtube video showing the inner working of an AI, including the pendulous vanes, neat: