Setting a repository owner means that whoever created the repository (triggered by pulling an image for the first time) retain their access to the repository even if they are removed from the pull-thru members team.
For proxy orgs this behavior is a little strange, since users indirectly create repositories (via pull, not push).

Note that this needs extensive testing, as it's unclear how Quay will behave around a repository without an owner. I have only tested the happy path and that at least worked.