Erm, no.

Demand *on Earth* will saturate before we're done mining the Near Earth Objects, which themselves are orders of magnitude smaller than the Asteroid Belt.

However, imagine the scenario:

The year is 2120, and some super-rich person *on Earth* wants to pay for some HUGE project in space. Who do they contract to do this project, and who's equipment and materials are used? The company who wins that contract will be *whichever* company was able to *double* equipment quickly, repeatedly, over the prior decades.

Now, consider that all your machines can be recycled, and that you own however much you can make use of; you'll want to grab and process all the asteroids *before* everyone else, and when you turn them all into mining-bots that's fine, because you will be recycling them once there is no asteroid mining left to do.

Finally, I never spoke of a "self-replicator run amok"; that's never been a valuable way to do things. It's not profitable. Rather, numerous factories would each process their own material, or stamp-out their own part, which are then hauled to other factories for assembly, just like here on Earth. It's called Agglomeration Economics, and it will always win against an *all-in-one-self-replicating* hodge-podge. Humans would still be in the loop. And, humans control robots; we don't *write code* telling those robots: "And here is how you can *change* your own goals, and here is how to disobey..." There's no realistic scenario with robots "running amok" - check the literature on the AI Alignment Problem.