I looked it up in kitzur
Hanging is specifically mentioned as an exemption, not bc of regret, rather bc we can assume murder ( people have a chezkas kashrus)
Of course this only applies to the chevra kadisha and not the question of how the mais will be treated in the olam haemes
But the hashkafic question is also contingent on a broader question of perspective. Do we look at the entirety of a situation or at a snapshot of a moment in time .
The person who commits suicide, at the moment of action we can say he was under extreme emotional duress and patur, but maybe the person spent a long time handling his situation poorly . Maybe his response to each nisayon was emotional wrong and thus the despondency with which he finds himself now is of his own creation.