Or even leaving aside slippery slope, any character--even a crazy one--has to have some recognizable behavior or else there's no character. Two-Face is an obvious example--he's bad, he's crazy, but his craziness follows a pattern. Only the Joker has no pattern, but that itself is a pattern. He's unable to be consistent for very long.
Which is not to say that a character like Jason can't cross a line he wouldn't have crossed before; the writer would just have to know exactly why he was doing it and what that meant for him. A lot of Jason's views on things, whether one agrees with them or not (and plenty of people love them) are fairly clear and important to him. He doesn't just say "fuck it", he has some reason why crossing the line is more in line with what he thinks. (Or else he needs some epiphany to change what he thinks. For instance, his whole experience dying etc. changed something fundamental in his belief system by destroying a kind of trust he had in Bruce.)
I don't think Jason could really be described, as he was elsewhere, as a thug who just wanted a chance to beat on people. He may accidentally become that, but it seems like that's always what he wanted not to be. In a way, it's what always made Jason more potentially dangerous than Damian who doesn't seem to really care.