Since Bitbucket 8.16 there is an ability to set pull requests to auto-merge. Besides configuring the merge strategy, it is also possible to toggle the "Delete <branch-name> after merging" option on the configuration screen, which is very useful, as it helps to de-clutter the repo branches.

Unfortunately there is no such option as "deleteSourceBranch", when setting pull requests to auto-merge vi the REST API: link. In our scenario this would be very useful, for the reasons stated above.

Please consider adding this feature, as the auto-merge REST API feels to be only half-implemented at the moment.