In a functioning society the primary mechanism to deal with violation of social norms is (temporary or permanent) social exclusion and in consequence the loss of future cooperative benefits.

To demand public humiliation doesn’t just put you on the same level as our medieval ancestors, who responded to violations of social norms with the pillory - it’s actually even worse: the contemporary internet pillory never forgets.

You think exile is a better first step than shame? That's certainly a take. On the internt, that does manifest as my suggested way of dealing with it, a curated space where offenders are banned -- but I would still advocating for attempting lesser corrective behaviour first before exclusion. Moreover, exclusion only works if you have a means to viably exclude people. Shame is something peers can do; exclusion requires authority.

Shame is also not the same thing as "public humiliation". They are publicly humiliating themselves. Pointing out that what they publicly chose to do themselves is bad is in no way the same as coercing them into being humiliated, which is what "public humiliation as a medieval punishment" entails. For example, the medieval practice of dragging a woman through the streets nude in order to humiliate her is indeed abhorrent, but you can hardly complain if you march through the streets nude of your own volition, against other people's desires, and are then publicly shamed for it.