Right now on our install we have a few states:
When a user moves a task between states they will become the defacto assignee. In general (personally) I can see the general wisdom in this default, but there have arisen a few situations where arguably showing the input with a prefilled in user (like when you go to normally Reassign/Claim a task) would make sense.
Yesterday I stalled an issue for someone because it had no assignee yet, and then suddenly I was on the hook :) It was an easy fix, but I think it probably would have made sense to show the hint that I was taking on the issue as I was shifting state on the issue.
One of our users requested this upstream issue so they could submit a patch to this effect.