Like either they go full tank or full AP, with the only exception being those hybrid items like Zhonya or boots. You don't have a lot people who go like Rod of Ages and then fulltank but you DO have people who go stuff like Black Cleaver or Titanic and maybe another item into fulltank. You have some exeptions to this rule from time to time but honestly not that often. So why is that?
A main reason why is because of auto attacks. Bruiser like champions are a mix of durability and damage. Too much of either sets them up as just a tank or an assassin. This means most are relegated to more of a sustained damage/duelist play style. while building 1 or 2 ad items you not only have abilities for small burst but autos to really cement the sustained damage role. Ap champions are harder to make fill the same role because of their reliance of abilities so much more than autos. This means that if they rely entirely on abilities there isn't a reason to not just build straight ap and have burst. The closest champs we have to this are battle mages like swain and vlad.
There are many reasons why AP bruisers are virtually non-existent. One of which is that many AP champions that have potential to be AP bruisers lack sufficient DPS through their kits and through itemization. Many AD bruisers can build 
or
and remain a threat through most of the game. Such an item combination doesn't exist for an AP bruiser to exist. The closest combination I can think of is 
which is nowhere near as strong as the item pairs above in terms of DPS or even survivability. With this combination you get 180AP (after ROA is fully stacked), which is 15 + 0.15*180 = 42 bonus magic damage on-hit from Nashor's Tooth - quite underwhelming. Not to mention, AP bruisers desperately need magic penetration by the mid game, the only decent option would be to build 
since there is no AP Black Cleaver, but Void Staff offers no durability and takes away a slot for more defensive items which are a must for a mid/late game bruiser. There's also the problem of mana issues and lack of sustain.
As mentioned, battle mages are the closest thing we have to an AP bruiser.
old sejuani
Diana is the only true ap "bruiser". But Diana works more like a mage/assassin since diana's only option is blowing up people. Rod of ages is just a garbage item. A ap bruiser item would have like 10% cdr, resistances, 30 ap ish and a unique passive
?
You have some exeptions to this rule from time to time but honestly not that often. So why is that?
Largely it's just player preference/adherence to meta. I enjoyed building RoA on multiple AP champions (I largely started maining support a few seasons ago, prior to that I was a diehard mid main) back when I played mid often. It's the same reason you rarely see Lich Bane- there's nothing wrong with the item but people don't want to use it too often.
They 'optimal' strategy for AP is to sit back, blast with mana, CDR, damage, and hopefully just never get caught. Tankiness, like Lich Bane, requires risk; something nobody wants to have.
On another note- a lot of tanky-AP champions simply aren't meta/"good" at the moment.
Typical top RoA then tank users:
I can count maybe a dozen of how many of those you could pick for top and not immediately have your team yell at you. And out of them, only a handful will be objectively better for it compared to other builds. I built RoA on Diana, that doesn't mean it's the best item for her.
Because Riot is incredibly lazy when it comes to developing AP items. I've posted on this before, but they're perfectly willing and able to come up with items for ADCs, assassins, and even tanks that attempt to fill different playstyles and fantasies.
But when it comes to AP items, they just put absolutely no effort. Every item they release seems to be "here, have more damage". And so itemization ends up being super flat and bland, and it doesn't work well for a lot of AP champions, like AP bruisers.
The reason is simple. There are no real "bruiser" AP items EXCEPT for Rod of Ages. The only other possible one we had was Abyssal Scepter and obviously Riot nuked that option. Rylai's and Liandry's could also be considered bruiser AP items but the problem with those two is there's not enough health in either and they only synergize with certain kits. You can't really have an AP bruiser without building damage and HP/armor/MR, and there are only a few options for all three in the AP category, with most of them being niche items outside of RoA. One thing though I never understood was WHY people don't build ROA. It's an amazing item, sure Ludens gives more burst, but it gives you lots of mana, lots of health, and lots of AP, making you a more durable mage. I personally love it on every mage that uses mana. I sometimes wish champions had mana so that it'd be a decent choice on them considering HOW MUCH mana it gives, it makes it extremely suboptimal despite wanting the health and the AP it offers.
Vladimir for example only gets away with being an AP bruiser because his passive allows him to build tank items and still get damage from it. That's the ONLY reason he builds like a bruiser, because tank items don't give AP, and there are no real AP bruiser items outside of RoA which he cannot build.
The AP items that also give health or resistances aren't typically what most AP bruisers would want.
The only exceptions I can think of are RoA (takes a while to get going, though) and Banshee's (but pretty much every champion would want to use it if they used AP, anyways, so it's a moot point).
I guess you have Mordekaiser, but he's more juggernaut than fighter (which is what I assume you meant).
Well, there are more champs that could go ap-bruiser if people actually would want to. 
for example all work great with 
for a total damage amp of ~26.5% and some nice aditional burn damage and a bit ap.
As for RoA into stuff, it just needs to long to kick in and delays important stats like CDR, while bruiser builts usually want pen or other damage amp to support their high base damages. If you look at cleaver, it gives cdr, %pen and mobillity, so stuff that amps you're kit quite well.
RoA only gives some solid stats with a delay and no utillity at all.
Another issue with roa is that is just the go to ap-bruiser item, giving some cdr, some %damaghe amp and solid def stats, and it shares the Eternety passive with RoA while also solveing most mana issues so you don't need RoA for that.
Honestly, RoA needs either to have something more outstanding once it reaches max stacks, or atleast eternety should be stackable so it feels better to pair it with abyssal.
However, in the current state of the game, sacrificeing more than maybe one item for offense will leave you to squishy to support tanky-dps patterns, so most of the time it's just more effective to either be fulltank or go full ap and just burst people.
Haven't you noticed Korean players build more on the tanky side; than they do pure damage?
> or 
Unless they're like a pure poke champ lol
A. There really are no AP bruiser items. AD bruisers get things like 
etc to build health while still gaining damage through passives or AD, especially since they can weave in autos into their combo.
B. Bruisers break items. Or other classes break items meant for bruisers. Riot has THE HARDEST TIME making an item that is meant for class X that doesn't immediately get cannibalized by class Y. Looking at you 
C. For AP bruisers to be a thing they would have to have high enough ratios to not just build full tank, while having those ratios not high enough to just build full glass cannon and try to assassinate people. Diana is a perfect example of someone who SHOULD be an AP bruiser. AP ratio on autos? Check. Shielding? Check. Ability to stick to a target? Check. But her ratios are high enough that you either go full AP and try to assassinate a target or you are useless because their really are not AP bruiser items.
Going to point out, in addition to everything said here, that the vast majority of champions who have AP scaling are ranged, and there is no such thing as a 'ranged bruiser'.
Ranged AP: 
Melee AP (Has to be divided further into assassins, tanks and bruisers): 
See the difference? The reason for this is because AP is associated with magic, not with brute strength like AD is. And magic is typically shown being cast by your hands or from a wand or something. It's something that weak, ranged casters use, not beefy warriors.
Like either they go full tank or full AP, with the only exception being those hybrid items like Zhonya or boots. You don't have a lot people who go like Rod of Ages and then fulltank but you DO have people who go stuff like Black Cleaver or Titanic and maybe another item into fulltank. You have some exeptions to this rule from time to time but honestly not that often. So why is that?
You have to first define what "bruiser" means. Bruiser is not an official riot class definition. It is a generic MMO term. Bruiser basically only means you have good damage mixed with good defense, but that's way too generic to be useful for LoL.
You specifically say you want AP champions who build some damage but then go full tank. That would typically describe juggernauts in LoL. You might also have some vanguard or even warden type tanks that can build that way and be effective, although I'm not sure if it's always optimal to do so.
Mordekaiser is the only AP juggernaut we have. BUT - he doesn't build the way you describe. He builds more like Galio, using hybrid AP/defense items primarily. Galio is a warden tank though. So even he doesn't want to build full tank.
This could be a problem with AP itemization in general that makes building a few damage items and then going full tank not a viable option.
Trinity force and Steraks, and the upcoming atmas, are all designed with AD juggernauts in mind. But the juggernauts themselves also have kits that tend to allow them to do more damage with less items to begin with. Maybe Morde isn't designed that way.
