Think of what fighters are to begin with: Divers and Juggernauts, right?
Alright, so when we say stuff about "ap fighters", who are we talking about?
This is the reality: 
Don't confuse Battle Mages with Fighter class champs that build ap. Two different things.
Ahpe1 votes
too
chipndip11 votesThat is a battle mage.
Ahpe3 votesHow is he any different from
Battle mages are like 
redniwediS1 votesAlright, let's quote the wiki a bit.
Divers are the more mobile portion of the Fighter class. Divers excel at singling out high-priority targets to blitz toward, immediately forcing those targets (and their teammates) to deal with the diver’s presence. Divers are not as durable as the tanks or juggernauts of the world, but Divers can take their fair share of punishment while bringing enough damage to be a real kill threat if left unchecked.
The first half of the Fighter class is the Diver. This is where Elise and Diana exist. Rumble isn't all that great at singling out high-priority targets and rushing them down. He can't lock a target like an Assassin can, and is better used controlling a fight.
Juggernauts are melee titans who relentlessly march down the opposition and devastate those foolish enough to get within their grasp. They are the only subclass who excel at both dealing and taking significant amounts of damage, but in turn they have a tough time closing in on targets due to their low range and extremely limited mobility.
The second half of the Fighter class is the Juggernaut. This is where Mordekaiser solidly exists. Rumble has multiple options for slows within his kit, let alone itemization, and can't take all that much punishment when focused down. Rumble cannot rely on base damage for anything but the extreme early game, and just doesn't fit into the Juggernaut subclass.
I could see him fitting into one of the two Fighter subclasses if he got a new kit, and I could see a kit like that being very fitting to his gameplay, but his current kit is simply not that of a Fighter.
Ahpe1 votesWell you forgot the types of juggernauts. Raid Bosses and Freight trains. Morderkaiser is a Raid Boss for sure but Freight trans are the less tank and just kind of run at you. I.E. Garen, Trundle, Udyr
Sure Rumble has ranges slows but Aatrox has medium-ranged knockups and a dash while he's still just an AD caster juggernaut(raid boss). Rumble got that W speed buff+shield and his passive gives him enhanced basic attacks which could reasonably make him the one and only AP freight train.
redniwediS1 votesThe "raid boss" and "freight train" are unofficial, and even so each one of them would have to fit the definition of a Juggernaut before they can fit those two categories.
Aatrox is a something, and honestly I'm not sure if he should be in the Juggernaut category. It has been years since Riot touched the classification system, and if they want to make Aatrox a true Juggernaut they might have to make some changes to either him or the class definition.
Rumble does fit the additional context of what a "freight train" is, but he still doesn't fully fit the definition of a Juggernaut. To add to that many, if not all, Battle Mages also fit that additional context, having weakish tank and primarily having to run straight into battle, which just so happens to be exactly where they want to be.
Sorry man, but Rumble is a perfect fit for the Battle Mage class.
Ahpe1 votesRumble is literally on the line between Freight Train and Battle Mage bro. If a freight train isn't a juggernaut then what are they? Just like any other freight train, he will just kind of run at you awkwardly like Udyr or Trundle and can AA you("can" because again he's right on the line so he'll burn you then punch you").
P.S. Aatrox is just kind of an Illaoi with CC, Illaoi is an AD caster juggernaut ¯ \ (ツ)/¯
redniwediS1 votesAs I said "freight train" is an unofficial term. It's close to both the Juggernaut class and the Battle Mage class because it's specifying particular attributes in a champion that do not necessarily dictate their place in League. It comments on playstyle, not the general balance and design goals that are what the champion will be judged by.
It is a useful term, but it is not a class term.
Also it's the CC that makes me question Aatrox's placement as a Juggernaut. Darius had the most CC of the main Juggernaut cast, closely followed by Trundle and Udyr when they were added in, and Aatrox has a lot compared to them.
Ahpe1 votesThen tell me what Udyr and Trundle are but not freight trains how they are any different from Rumble except for a little bit of battle mage in him.
redniwediS1 votesI already covered all of that.
The term "freight train" is not official. It is not a class, and is not based in the design philosophy of that group of champions. Classes describe design and balance philosophy, and that is not what "freight train" does.
Udyr and Trundle are Juggernauts. Rumble is, by definition, a Battlemage.
Battlemages get into the middle of the fray, seeking to wreak havoc upon the entire enemy team with their overwhelming sustained area damage. Due to their relatively short (but not melee) combat ranges and the need to burn down their opponents over time, Battle Mages have significant defensive capabilities that range from sustaining endlessly to literally defying death for a short period of time.
Ahpe1 votesThen why does he have the ability to run at you and have sustain AA damage against you like Trundle while also having sustain AOE damage. His P and W make him a juggernaut while his Q and R make him a battle mage. Rumble is the line.
Btw doesn't have significant defensive capabilities
redniwediS1 votesVery few champions are the definition of their class. They all exist slightly away from the definition, and by doing so become unique and separate from other members of their class.
Rumble is the only melee Battlemage. To compensate him for his lack of auto range he has bonus auto damage, but that doesn't change his Class. All Battlemages run you down and kill you with sustained damage, and they all do it in their own unique ways.
And significant defensive capabilities can mean CC, defensive stats, sustain, or any other number of things. You try chasing an Aurelion Sol as a Juggernaut and tell me he doesn't have the tools required to defend himself.
Ahpe1 votesBecause of his lack of range that makes him part fighter.
Yes having CC is a reliable defensive capability but then you're saying all these champions have reliable defensive capabilities solely because their hard CC:
No shit a juggernaut is going to have trouble against , his kit is for kiting and you're suppose to be able to kite juggernauts. Q and R is nothing when 
hops on your ass.
redniwediS1 votesAurelion does have significant defensive capabilities. They are not capabilities that stop a Diver or Assassin very well, but that does not make them insignificant.
And that is what I'm saying about that CC. If it is reliable and can save their lives then yes, it fits the definition I used. Not all of the champions you listed have reliable CC, or CC that is particularly useful in a defensive manner, but there are a few there that do.
Rumble fits the definition of a Battlemage to a T, just as other Battlemages do. He also has additional aspects that set him apart from the other Battlemages, just as the other Battlemages do.
He simply does not have enough Fighter qualities to be part of either Fighter subclass.
Ahpe1 votesI keep repeating Rumble has the ability to run someone down and AA like a juggernaut as well as run someone down with AOE like a battle mage.
Mordepool2 votesHe does have an AA reset on his Q
Hyquiem1 votesAurelion isn’t a battle mage due to his dps. An ap fighter is somone who’s going in and ether hammer doom or dead broom.
Paroe1 votes... A fighter is a broad main class. Not a specific sub class. Really people, what is so hard to understand there? Do we call soldiers by their specific training types ONLY? Does the broad term not exist?!
Fighters are melee champions whose itemization leans towards AD/AP+resistances. Bruisers are fighters whose itemiations leans towards HP+AD/AP and who have mobility. Juggernauts are fighters whose itemization leans towards HP+AD/AP and who do not have mobility.
Battle mages are just AP bruisers.
That being said... Diana is an AP fighter, not a battlemage, as battlemages are charazterized by spammy kits like those of Ryze and Cass, not the more "i got a pick!" kit of diana or Akali.
Theres four main types of champions; AD AP Tank Marksman
Of these four, there are main classes. Fighter, melee champions. Mage, ranged ability champions. Tank, anyone who buys HP items as most of their build. Marksman, anyone with over 500 range who uses attack speed, AD, and critical strike chance.
Of THOSE classes theres sub classes which also bleed over into other classes. Juggernaut and bruiser for example both bleed into tank, but bruiser also bleeds into assassin which also shares a place with the mage class. It'd take a skillfully made venn diagram to ACTUALLY show how the classes look; its that messy.
chipndip11 votesBruiser actually isn't an official term. It's really just used to cover fighters and skirmishers together as it is now.
redniwediS1 votesFighter is an official Class, and has an official definition. It has two official subclasses, Diver and Juggernaut.
It's not a broad main class, it is a well defined class with specific strengths, weaknesses, and a design philosophy that covers how Riot looks at the group of champions that all fill a similar role.
