> Making precedent binding seems a bit crazy, to be honest, because if the precedent contains mistakes (which it inevitably does), then those mistakes become binding also, right? So logical inconsistency and contradiction is inevitably part of the common law system?

It is also not the correct institution to "make law" I think. It does not represent the population in some way as in a representative democracy should be. It was not debated in the parliament and it was not campaigned on. It is in some way a rule of experts.