No, it’s not possible. Mu can be used in ranked though (and Story is how you unlock her). You get unlimiteds from Score Attack.
Um, if you’re really having problems with Beginner Mode players, I’d say you have a LOT more problems than just “Hakumen spam.” Just about everyone I know that plays says Beginner Mode is only good for button mashing, which is easily countered if you know what you’re doing. Granted Hazama isn’t exactly an easy character to pick up, but still, it’s not like it’s impossible to beat button mashers with him.
Also, “spoon feed noobs and not encourage getting better”? Tutorial and Challenge modes exist for a reason.