The short story

It would be nice if branches were auto-deleted after a PR is merged.

Long version

You can have head branches automatically deleted after pull requests are merged in your repository.

https://docs.github.com/en/repositories/configuring-branches-and-merges-in-your-repository/configuring-pull-request-merges/managing-the-automatic-deletion-of-branches is the relevant documentation. https://github.blog/changelog/2019-07-31-automatically-delete-head-branches-of-pull-requests/ is the relevant changelog entry.