“Are you denying that there are a lot of legitimate claims of abuse?”
No. My only point is, simply, that to adjudicate the claim (to determine whether the abuse allegation is true or untrue or any other claim) Al Pi Halacha ONLY a Beis Din can make that determination and that it is strictly prohibited to litigate that or any issues in non-Jewish courts or to use secular judges or to utilize any laws other than Torah law.
“My question is in THOSE cases. He know the truth. Is he a bad person for keeping her in a chanied marriage. Even if strictly speaking as far as even haezer goes he is not obligated to divorce her?”
If he abused her of course he’s bad. I’m not sure why you need to even ask. In order to correct his behavior he is required to stop abusing her. The Shulchan Aruch says that if Beis Din ascertains that it was proven the husband was beating his wife the Dayanim are required to order him to stop. And that if it is proven he continued beating her after being warned by Beis Din, the Halacha is the Dayanim can force his to divorce even if he doesn’t want to. That’s the Halacha clearly stated in Shulchan Aruch. If you’re asking regarding a case where he’s beating her (which he obviously knows) but the Beis Din has no proof of it, then of course he’s being bad and is required to stop or agree to divorce (even if Beis Din can’t force him since there’s no proof.)
But if there’s no proof we can’t accept the allegation as true. The Halacha in S”A is clear about that.