Depends on the BGA; the extremely high-density ones generally require special tools. They're also nearly impossible to inspect without special camera equipment. The really low-density ones (like DFN) are pretty easy for a hobbyist though, but in general BGAs should be avoided for designs aimed at hobbyists. You can get away with repairing them sometimes, using a reflow oven (made from a toaster oven), or even a hot-plate, and it is possible to re-ball them at home, but I wouldn't count on this as a reliable thing.

"BGA at home", I'd never touch that. A person w/o experience and/or rework station is likely to meet frustration only. It's a futile effort in my opinion.

The inspection part is bang on - what if there is a short and it just burns the traces. Now the thing is not repairable even by a professional repair service.

I am just a programmer... totally for right to repair, open schematics, easily to source components, etc. I can repair electronics, incl. SMD soldering on laptops, LED light fixtures, diagnose home appliances but I'd not touch any BGA. Or heat pump water/fluid subsystem or high pressure vessels -- and I'd prefer if I'd buy a house with any of them installed not to have been repaired w/o care and experience.