Then the question is, who should get to decide when to replace a judge? Obviously not the executive branch, especially in the context of this particular discussion.
For example, some judges are elected (probably varies by state, but there are some places where that's true), so in those cases a perfectly viable remedy already exists (in theory, at least). Of course, in practice there's nothing to prevent voters from being very pro-prosecutor. Usually the judicial system is the best option for a remedy to that sort of problem, but of course then we're back where we started..
Typically the legislative branch handles impeachment, although in some states the judicial branch would also play a role in the process. We have a norm that officials are not fired for doing their jobs poorly, even to the extent that they intentionally harm people, and that certainly makes various things run more smoothly. Smoothness would have been a more convincing argument back in the day when our government produced acceptable results [0], assuming that day ever occurred. Obviously one would prefer that people not be convicted of murder based on stories told by buffoons about their interactions with dogs. Probably there aren't a great many judges who would allow such a thing. When that has occurred, however, a public proceeding in a legislature would constitute a wonderful reminder for all judges to take their heads out of their asses, which would contribute to justice.
[0] In USA we spend twice as much on health care as any other nation. Our performance against covid has only been better than Peru, Brazil, and several nations in eastern Europe. Every nation in Asia and Africa had fewer deaths per capita than we did.
For example, some judges are elected (probably varies by state, but there are some places where that's true), so in those cases a perfectly viable remedy already exists (in theory, at least). Of course, in practice there's nothing to prevent voters from being very pro-prosecutor. Usually the judicial system is the best option for a remedy to that sort of problem, but of course then we're back where we started..