AP Bruisers will always be a balance nightmare with the current set of items
When you look at champs like
etc. you always see them dominating the game and warping the meta around them or they are just straight up irrelevant.
Right now Vlad is broken and is terrorizing the game. While any other one on that list is irrelevant.
I think the biggest reason why these champs are so hard to balance is that they have nothing to be balanced around.
Imagine the current AD Bruiser roster and what they build. You are thinking about stuff like Steraks / Titanic / GA / BC / Trinity and all that good stuff. Items that benefit their kits and synergize with it. Now Imagine if we just removed those items and these bruisers would be stuck with items like Ravenous / BotRK / Mallet / IBG / Maw / QSS You already know that this would be absolutely horrible for any bruiser out there that isn't named Mundo.
Now those AD Bruisers just build suboptimal stuff and just deal not enough damage to be relevant. So they start building ultra damage items like IE and ER so they deal enough damage but are not tanky enough and die in 3 seconds.
Then Riot comes in here and either buffs their damage or tankiness, the problem is, if that happens then they become unstoppable. When you give them enough tankiness that a Darius with IE and ER rush can survive then he will instagib anything that gets close. When you give him more damage then Darius will just go nigh full tank and still kill anything that gets too close.
It becomes super hard to balance these AD Bruiser because the items they build are not working with their kits. IE is not designed for bruisers but when there isn't a better damage item then there just isn't a better damage item and they are forced to build it.
When you look at what items the AP Bruisers I listed above build on OP.GG you quickly realize it's stuff like Ludens / Rabaddons / Spellbinder, stuff that a Bruiser wouldn't build if they aren't forced to do so.
In short, if an AD Bruiser would build the same as an AP one it would look like this:

It's this mish-mash of suboptimal items that you hope kind of works on your champ and if it doesn't then good luck staying relevant in the game until the day Riot decides to make it work, in which case you become unstoppable.
It is also very clear that these AP Bruisers have certain parts in their kit that just could be on an item they could build. Sylas and Diana passive for example, they are more or less tiamat effects... how about we make an AP Tiamat item and give these champs actual passives. Passives that aren't here to forcefully make them work with the current suboptimal buildpaths they have
Mordekaiser passive too, that could be an item, you could remove Sylas shield if that item was a thing. Then Sylas E wouldn't be so grossly overloaded and wouldn't need to be an a 18 second cooldown lvl 1. But he needs that shield right now, otherwise he will die in 3 seconds.
Same with Ryze shield, do you see a single shield in Darius kit? Or shields in other AD Bruisers? There just a few of them. they don't need it because the items they buy cover that aspect (Steraks).
When basic needs of a class are not represented in the items they buy then all of those things need to be forcefully included in their kits otherwise the champions wont ever work.
If you want to make actual AP Bruiser and not pseudo tanky burst assassins on their good days and walking wannabe AP tanks on their bad days, you need to rip off their innate champion mechanics that the whole class needs, put these on items and give them tools or strengthen them into wanting to buy those exact class defining items.
Only then you can actually make them into normal champions that aren't a balance nightmare 24/7.

(the real one not the fake one)


+
is pretty much unviable and is nowhere near as strong as taking a combination of 2 of:
. You get outscaled so quickly against AD bruisers if you try to actually build as an AP bruiser with what the current itemization offers. So you're forced to build as an AP nuke and hope you can get as much damage out as you can before you die. Some key points with poor itemization for AP bruisers:
for a bruiser build, but that's as ridiculous as buying
for an AD bruiser build. So you're forced into building flat pen, the easiest source being
which is both a blessing and curse. Great item as it gives you early pen, but most AP champs are near reliant on Sorcerer's shoes to do relevant damage, meaning that
and
have true damage and/or built in armor pen; while
have mixed damage; 
have absurdly good synergy with conqueror (along with the aforementioned Jax, and Irelia); and
have % max health damage to keep them relevant.
, which is weaker on all AP bruisers you mentioned. Hextech Gunblade is literally an Akali and Katarina item.
is more of an AP assassin / poke-mage item that easily gets popped these days from things like a stray Luden's proc.
is really strong but again offers very little defense outside of its passive. You only buy it for its passive because time is critical in this burst meta. Apart from its passive, it offers as much protection as
for AD bruisers, and you rarely see Maw built on AD bruisers despite the buffs it has gotten. So if you want to be beefier, you need to dip into tank items. But AD Bruisers have the luxury of being able to buy tank items without their damage falling off as hard, unlike AP bruisers.
are forced to build mage items and be played as assassins.
The same is true for Juggernauts, where champions like
only really have to build one or two of the above items and be a monster while
/
and probably now
from abusing AP bruiser items? How about mages in general?