In your first example it seems he’d be halachicly obligated to give a divorce. Clearly he should give it. And if he doesn’t and Halacha permits coercion then he should be coerced.
Your second example is a bit vague. Halacha has situations where he must give it and can be coerced if he does not. Halacha has other situations where he’s halachicly obligated to give it but the Beis Din is halachicly prohibited from applying coercion. In such a case he’s a rasha if he fails to give it even though the rabbonim cannot apply pressure and can do no more than tell him to. Then there are cases where (Chazal and) Shulchan Aruch say he does not have to give a divorce his wife is asking for and B”D is to tell her to return to his home and their marriage. Chazal, the Mechaber and others enumerate such situations.
No lack of sympathy was expressed. Criticism was expressed for those that exert pressure for a divorce in situations where Halacha and S”A rule that one needn’t be given and pressure is kneged halacha. And when the term aguna is inapplicable even though it is bandied about to create secular pressures that are a severe violation of manifold halachos.