My personal rule of thumb is that I don’t trust anybody whose Twitter profile picture is a photo of themselves.
My Twitter avatar is a picture of a fractal I generated with my own software. That reveals (fuzzily) a certain non-obvious aspect of my personality, which you couldn't get just from looking at my face. The majority of people have faces; mine isn't much of a signal to strangers.
Faces are for recognition. If we met at a conference, you could recognize me again by my face. If you don't know me, my face isn't very useful unless you expect to meet me in person. So, a face on Twitter is unhelpful to the point of being counterproductive.
Anyway, that face might not even be theirs.