Definitely. I haven't put on my super costume since the no-super category for BP was created for a reason...it's boring.
In general, no one loses anything by having multiple categories with whatever limitations people want to add. No Item is an obvious one, but there are other possibilities, such as no-skips/no-glitch, no leveling, etc. I play Soulsborne games and it very much seems like their popularity goes hand in hand with the multiple challenge-runs and speedrun categories...no reason to avoid it here.
Every runner I've ever seen run DMC games uses turbo (including myself). It does make combat harder, but also more rhymthmic (which IMO helps me play better).
Try getting used to it via Bloody Palace first, then running with it...you'll never want to play at default speed again.
As a Bloody Palace runner, I have to agree...I would prefer the super costumes to be their own category. I use it in my runs because essentially I have to, but I would run it without if there was a separate category for it.