Your another point is that it is difficult to find good teachers for baroque flute locally, which is very true since it is not a popular instrument. But the situation is different from piano. You can for sure find adequate piano teachers in every town.
I am not so sure that adequate piano teachers exist in every town.
And finding them requires sorting them out from the large number of hobby piano teachers.
It seems very likely to me that skype lacks some of the advantages of F2F teaching.
It seems very likely to me that quality teaching is hugely important.
I would rather have a superb teacher over skype than a poor teacher in person. Is there a point at which a mediocre teacher in person becomes a better choice than a superb teacher on skype? I'm not sure. I'm inclined to think nothing outweighs the teacher quality parameter.
If you have special requirements you may have no choice. Maybe a pianist with carpal tunnel or neck problems needs that one teacher who has success with this, or a brass player with an upstream embouchure, etc.