Hi Tigermoth
I don't think that a father who has no official history of violence or controlling behaviour should automatically lose unsupervised access to their children forever, but I certainly think any access should be heavily supervised for quite a while, and that such men would have to show that they are no longer so hostile to the mother of their children, that they are overcome by the urge to beat them to a pulp every time they see them.
I also think we have to take into account the (conservative) statistic that the average battered woman has been beaten up seventeen times before she even contacts the police, let alone is willing to stand witness in a prosecution. Just because a man's violence is officially unregistered, doesn't make it any less dangerous and damaging.
I think that as a principle of re-habilitation, men do win back the right to see their children un-supervised, but I think it has to be when their children are old enough to defend themselves against any potential violence and when the men have enough mastery of themselves to acknowledge their own responsibility for their words and actions. As you suggest, it very much gets down to individual cases, and I would always err on the side of caution - the safety of women and children in civilised society would take priority over the aggrieved feelings of men. And no-one is suggesting that even these violent and dangerous men can never re-habilitate themselves - a man who is truly sorry for the havoc he has caused in his family in the past, and is facing up to his responsibilities, would surely be prepared to accept that his past behaviour has made him unfit to be in sole charge of his children without stringent safeguards being applied. After all, most men, even these very violent ones, would be horrified by the thought of another man being in charge of their children, who had done the same thing as them - they'd probably be the first to jump up and down shouting blue murder about the ex-missus getting herself a new boyfriend who is known to be handy with his fists. And they'd have a point!
It is a complex area, and there are no hard and fast rules, but what I do know is that currently, the very real and present violence of men is going unheeded and unpunished and children and mothers are going unprotected, while we theorise about situations in which men would be penalised by a matriarchal man-hating law which is never going to exist. Domestic violence is still not taken seriously by the courts, by men and by society. And because of that, there are so many cases of children being terribly damaged by being forced into contact with men who have never been made to confront the shocking abuse they have inflicted on their children and so continue to blame the women who were their victims and use their children to control those women. However it's done, I want that situation to stop.