I've had essentially that - if a bit fancier to accept an optional argument as well as handle common "mainline" branch names - aliased as `git lint` for a while:

    [alias]
        lint = !git branch --merged ${1-} | grep -v -E -e '^[*]?[ ]*(main|master|[0-9]+[.]([0-9]+|x)-stable)$' -e '^[*][ ]+' | xargs -r -n 1 git branch --delete

    git pull --prune && git lint