That's assuming you'll even be able to find non-brand replacement parts. Figure that the wear and tear on an autonomous vehicle should be even more predictable than current service intervals, and these vehicles can drive themselves in for service. Manufacturers and their dealer networks stand to win back a much greater share of vehicle service and repairs than they get now. With that shift, independent mechanics may become a thing of the past.
...And that's the "benign" version. Before we get to that point, my guess is that automakers will increasingly push leases and similar arrangements over actual ownership, to the point that it becomes a matter of managing "their" fleet, not servicing "your" car. Magnuson-Moss compliance won't be an issue; you won't have a say in who does the work because you don't own the vehicle. There could also be upsides to this model, e.g. after a wreck the company might just send you another (refurbished, but otherwise equivalent) car instead of making you wait on repairs.