But having every warning be public knowledge is a bit excessive, that is not to say every warning is justified but such a scenario will just create a scenario of "he said" "she said" "they said" which will just create a mess or rumors, lies and half truths.
I've been on other sites where you can click on someone's profile and the reason for why the person is banned is put and there isn't anything started from it, as long as it's subtle and doesn't go into detail, then I doubt that anything bad will come from it