Personally, I think it's a good thing when champs are able to play more than one role. It allows their mains to play them more often.
No real argument there.
I main support and the pool of viable champs right now is possibly the highest in the game for any role. So I don't think it would hurt diversity at all.
I guess that really depends on what your definition of viable is.
I'm more concerned about the champion pool with their primary lane being support. There's a small handful of support primaries, being the smallest champion archetype of the 6. There's a small handful of tank/supports and mages that really feel at home in the lane beyond that: resulting in a small champion pool overall. There's also the whole Lulu thing where she's a better top lanner than support.
Compare that to jungle where essentially every melee-range champion in the game can work that as their primary lane position, mid lane where the fairly massive pool of mages along with ~half the assassins feel at home, or top lane where a rather large mix of tanks, fighters, assassins, mages, marksman, and support champions all feel at home.
support just doesn't have a large champion pool. The only lane position it really beats is ADC.
I don't think this would make Braum a better alone champ than support at all.
It certainly sends a message he's better alone though, which is the bigger issue.