However, I think it may be beneficial to turn it on.
Often we forget to delete the branches, leaving many stale branches hanging around in the repository which may be confusing.
Manually deleting the branches is another manual step we need to remember to do, which is easily automated by turning this on.
There probably are not many cases where we do want to keep a branch after merging.
In the rare case where we do want to keep the branch after merging, we can manually click the "restore branch" button.
Deleting the branches is important for the automated PRs right now, otherwise it appears to reuse the existing branch for new PRs (I know that's not ideal, but it's a tradeoff we have right now for avoiding creating duplicate PRs).
Currently we don't auto-delete branches on PR merge across our repositories:
https://github.com/canonical/solutions-engineering-automation/blob/31296eb8d62358c5e66b7affea331931b37081c7/terraform-plans/modules/GitHub/settings/main.tf#L30
However, I think it may be beneficial to turn it on.
Docs: