Pros: you [sort of] own your Fediverse identity; you can make any changes to your instance you want (if you know how to do it); you’re in control of whom you peer with.
Cons: maintenance burdens (especially if you make any changes); content discovery complexity; possibly slightly less privacy (as you’re the only user of the instance, whatever is visible about it can be directly attributed to your activity). All solvable, of course.