You were onto something with your oak trees -> ship masts example but did not see it through. Just as the assumption that running out of suitable oaks for ship masts would hamstring seaborn commerce failed to foresee steam engines, I feel your objections to humans mining the asteroid belt (money, artificial gravity, etc.) fail to foresee intelligent machines not having any need for any of that stuff.
If you're AI housed in self-replicating robots, space is not so inhospitable. We send many times more machines into space than people because it's a good deal easier building machines to be hardened against radiation blasted vacuum than it is to protect human physiology from those challenges.
AI in control of self replicating robots, possibly nanoscale ones, need not concern itself with the economic viability of obtaining metals from asteroids as the payoff for the endeavor is survival and expansion. The travel time and energetic requirements are greatly reduced if you can afford to take a long time getting there because you don't have human passengers who need to eat, drink, breathe, sleep, etc.
If we're talking about the biggest assumptions in scifi, that humans will continue to occupy the top of the food chain indefinitely has got to top the list.