With custom user picker fields, you can choose particular people as the default user.

But, as a Jira user, it would be interesting to be able to have the default value of the field as "Unassigned". The default could be applied if the field is empty upon the transition starts or placed during the issue creation.

There is a simple workaround, but not practical:
Create a simple user "unassigned" or "none" that will be pre-filled by a workflow change.