People change due to criticism all the time, it really works. If criticism didn't work we wouldn't have so strong urges to do it, the feeling to criticize others is something we evolved to have.

Criticism might not change people the way you want however, it is like punishment vs rewards, you can change people by punishing them or rewarding them, both works to change people but in different ways and often punishment makes the person resent you so you should do it sparingly.

This is wrong in an important way (that's quite relevant to message boards like this one, about which you'll often hear that arguing about controversial subjects is pointless because nobody ever changes their mind). Basically, nobody ever individually changes their mind in the moment, so it appears as though debates are ineffectual. But that's only because people change their minds slowly, in private, in response to thousands of inputs.

And it might not even be the person you're talking to who eventually changes their mind. It might just be a reader, a thousand of whom exist for every one person visibly contributing.

You can't see the mind changing, but it's wrong to conclude that therefore it never happens.

In my experience, people generally cannot tell the difference. It's possible that I'm at fault in my approach, though.