As for forcing her to take the get, you’re correct. In such a case, I assume they would use a heter meiah rabbonim for the man, and the woman would be unable to remarry. That is not an agunah case.
It is in fact an agunah case, because it is really hard to get a heter meah rabbonim, and to get a bad one costs 50k and is almost certainly assur.
And the fact that nobody cares about the male agunos, is deeply disturbing.