Mahony is retiring this year and a coadjutor (who will succeed him) has already been appointed. He was kept in place in LA because there were massive lawsuits going on and it was felt that he created the problem and therefore he would have to be responsible for handling it. There is, furthermore, the possibility that there will eventually be criminal charges against him in one of these cases (facilitating the escape of a child-molester to Mexico) and he is not being allowed to slip away.
Mahony was very popular with the press and local Dem politicians because he is very, very liberal, to put it mildly. However, even that popularity has been wearing thin in recent years, and it will be interesting to see how this plays out once he retires and if the criminal case ever gets moving.
One of the problems with Law was that the events did not happen under his watch, as they did with Mahony, but Law became responsible for them and their earlier mishandling by people who were no longer there (in some cases, because they were dead). He became a media target because he was perceived as relatively conservative, much more so than the bishops under whom the cases had actually happened, and also because some people clearly resented his attempts, bumbling as they may have been, to resolve certain situations from decades earlier. Because he was not particularly well-spoken and was clumsy in dealing with the media, it was very easy to make him the fall-guy for many years of mismanagement, and removing him and replacing him with somebody who was savvy enough to manage things more smoothly was probably a good decision. I don’t particularly like O’Malley, but he has been able to get through some of this backlog more effectively.