We might not spot it from earth, but if we’re confident enough of where we’ll find it, its orbital parameters, its mass, a probe could be sent, and it could be detected through its SOI, and perhaps even direct observation.
Sure, ~300AU is a long way, but we have the technology, and it’s our closest black hole candidate by many orders of magnitude
If it is a choice between, (1) Spend $500M just to see whether there really is a black hole there, or (2) it is probably a just statistical fluke -- it is not hard to guess which will be chosen.
Sure, ~300AU is a long way, but we have the technology, and it’s our closest black hole candidate by many orders of magnitude