The same can be said about many, many other "online mobs".

Yes, because not disagreeing is considered assent. Telling people with stupid ideologies that their ideologies are stupid is not something you want to avoid entirely, at the very least to remind folks that they haven't found the One True Ideology.

Whether the ideology in question is SJWs/ctrl-left or alt-right... doesn't really matter. Neither of those should dominate the public or wield governmental powers. And to avoid precisely that from happening, you speak out against it.

Also, it is difficult to ignore people who can attack you offline. I think these fanatical students (seems to me they are usually students; students are most susceptible to recruitment in all kinds of cults) constitute pretty much zero danger to me... but they can be quite dangerous to their classmates, so if I had children in university age, I would probably worry a lot.

If you told me that when I eat pizza that it is a cultural appropriation, I would just tell you to f.off. But when a student is surrounded by militant classmates, this can lead to bullying. And even worse, when a teacher is a part of some social justice cult. So... not feeding the trolls is sometimes not an option, unless you want to give up on your diploma, and the time and work spent so far studying.

Not feeding trolls also assumes that people are mature enough to recognize who is a troll. But there is a continuum between people who sincerely believe that political correctness is simply the usual politeness applied to politically sensitive topics... and people who throw a hissy fit whenever someone disagrees with their latest pseudoscience. Try to make a line somewhere, and people who are under the line but quite close to it are going to object.

If the cultural appropriation people win, they end up promoting an expanded racial and ethnic segregation as a consequence. The mixing, remixing, touching, learning from by experience and adoption of culture is a critical element that works against physical segregation.

FWIW, I do support restricting people's ability to communicate online, in particular their ability to spam me. I'm not talking about global censorship, just me personally, and if someone actually likes spam, then they can enjoy it for all I care.

Even the event you mention probably depended on many being able to participate without risk, since one guy alone doesn't make for a very convincing 'mob'.

There are arguments for anonymity online, and I tend to agree that they outweigh the problems. I think it'd be strategically better to focus on these than try to attack the rather intuitive logic at the core of such calls for ending anonymity.

I disagree. Mobbing existed before anonymity; in fact, it was very much the norm -- the concept of "honor" is often tied to public displays of condemnation for the "dishonorable". Publicity makes it harder for people to disagree with what is perceived as the opinion of the majority, as unpalatable and uncivilized as it might be. This is why political votes are secret, among others; or why the Gospels explicitly warn against public displays of faith.

Every group of people will have its "dishonorable" enemies, and will always be keen to publicly shame them. Forcing people to attach their public identities to online activity will do nothing to dissuade people who see such actions as a badge of honor, but it will chill the display of dissent from the status quo.

Mobs existed before because there were so many people that you were effectively an anonymous member of it. Similar to behaviour in protests today.

However removing anonymity today would be difference since everyone could see your name and could get you fired, killed etc. Hence the OP is right that you would see less mobs.

Removing anonymity will just reduce the possibility to express a dissenting opinion. This is why authoritarian systems the world over have always loved ID cards and the likes.