Why are AP bruiser items so rare?

Because AP itemization is really bad at being diverse.

because then burst mages will become tanky; AP bruisers have the same problem juggernauts do, wherein when itemization catered to them will be good on them, another group of champions will break it.

sometimes i feel like riot want AP = Burst only and AD = High sustained damage

that's probably how it should be. AP DPS champions have been the most problematic group of all mages.

I'm curious what makes you think they're rare.

What exactly are you looking for? There are currently so many items that give AP with Magic Resist/Armor or especially Health.

To keep champs like Ahri and Brand from running around with 3500-4000 hp, while still bursting down squishies and perma-kiting bruisers and tanks. Plus, do you really want Kat, Akali, Fizz and Ekko to be able to build tanky without sacrificing any damage?

because ap bruisers can dip into tank/juggernaut itemization

for example

Most AP champs need to use a lot of abilities and mana and bruisers usually have extended fights so mana gating becomes a problem