The issue with AP bruiser's as a concept is that they have to do a good chunk of AP damage, roughly on the level of an AD bruiser. The issue is that they are limited by their cd's, which lead to a need to boost their scalings so they output the same amount of total damage. This causes building them full AP to be highly effective as they turn into an assassin, ex. Diana. Despite having her highest AP scaling being on her aa oriented passive, she can just hit minions twice then combo a champ 100-0.
The other option is not boosting their scalings and instead boosting their base damages. This turns them into tanks that like to build a ROA first. Best example being Maokai, who has the kit to be a bruiser but functions best as a full tank with just a touch of AP.
The closest we have gotten is Evelynn for a bit, due to her consistent DPS. However due to a variety of reasons she never functions best as a bruiser, instead having varied between Full damage through either AD, AP, or Hybrid, or functioning best as a Tank.
The lack of aa's means that you have to balance their spells to be auto attacks, but can't let them weave in auto attacks without disrupting that flow. On top of that they have no way to build their equivalent of lifesteal (gunblade) because an AD champ with AP scalings will make better use of that than an AP champ with AD scalings due to the ability to weave in auto attacks.
It's just a whole mess of issues that would probably require an entire AP bruiser item rework just to let a new champ thrive in that role, which could simultaneously upset the AP balance in other areas.
IDK, maybe if they gave a melee champ aa's that scaled with AP instead of AD or something.