Does anonymity give rise to hostility?

In my own experience, a large number of people on Wikipedia misuse anonymity to act in a way they would never act if everybody knew who they were. I acknowledge that for some people anonymity is important (e.g. users writing in topic areas that reveal their sexual orientation; people using their work time to write Wikipedia articles). But after being a Wikipedian for nearly four years now, I've come to the conclusion that the bad side of anonymity and sockpuppetry outweights by far the good side.

So, how about improving the registration process and testing the new feature for 2–3 months? E.g. Five out of ten users get an invitation to create a user page and upload a picture; afterwards, we track how many of them got involved in conflicts with other users (compared to the group of users who were not invited to do so).

Any other ideas how to measure success?

That's actually a pretty direct way to test it out, and it makes a lot of sense. Just make sure we test the pilot group against some kind of control group (I think that's what you meant). We can probably understand a lot about their experience from watching their activity at different types of pages (article space, talk space, project space), and particularly pay attention to their involvement in Wikiquette Alerts and what not.