I discourage people from using path parts, because git actually treats it like a path—and I’ve seen some conflicts with this. Better to just use hyphens as separators and forget that you can use slashes at all.
I'm starting to like slashes in branch names. They are so easy to visually grasp a list of branches.
Do you recall any of the problems you had? I'm frequently using checkout/rebase/merge workflow and never had any problems. But I always felt I am not using all features got had to offer.
I had a recent situation where someone had created a branch called `something/some-reason` and I had a branch called `something` that already existed locally. I was unable to check out `something/some-reason` because `something` already existed as a file.
Slashes in branch names are BAD ideas and should be avoided.
Totally agree on all lower case.