Although I can make the exception for Leblanc. Why? I actually don't know, lol.
She looks a lot like a mage.
Doesn't play at all like one though.
I don't know, it's just a weird bias I realized I had. What's your guy's take on this?
My take is mostly I don't agree with Riot's mage tag indicating "lots of magic damage and benefits from AP".
It would be one thing if champion tags simply extended to HP, AD, and AP scaling lines with tank/marksman/mage, but with 6 archetypes and many lacking a core scaling pattern or dedicated damage type, kind of wierd to point out an entire playstyle with magic damage as mage.
To me, mage is more about using a combination of range and CC to survive long enough to get things done, a general rocket-launcher power spike where you have big bursts of power but limited ammo, and a big focus on team-fighting and Area-effect explosions. If nothing else: mages are good at taking on crowds, with good AoE and good crowd control.
Also the term mage generally indicates a certain level of mechanics that makes a mage player feel smart and wizardly rather than like a drunk guy throwing fireworks at things, but that can fall through in a lot of games. Annie and Ryze doesn't really make you feel smart.
LeBlanc, Diana, and Katarina all admittedly have some of those qualities.
Akali doesn't really have any mage qualities, and I'd still quantify Akali and Diana as an Assassin/Fighter though.
With assassins: assassins seem all about speed. Having enough speed to survive instead of having a reliance on range or defense, in particular having mechanics that allow a champion to never stop moving while killing things: usually with resets, multiple dashes, and especially with fast combos and swift casting animations.
Assassin also generally indicates solid 1v1 potential and the capacity to take out a carry, often at the expense of lacking team-fight potential.
LeBlanc generally strikes me as more of an assassin than most due to meeting all the assassin criteria, and by contrast gives up pretty much every mage quality where both archetypes overlap. LeBlanc is beyond terrible in 5v5 fights, as she struggles to take out more than 1/5th of the enemy team's collective health. And any situation she can exceed that: you're looking at pentakill potential for most marksman, mages, assassins, and fighters just due to their better AA power, AoE, and resets.
When thinking about this, I realized how broad of a term "Mages" are.
Obnoxiously vague, yeah.
meanwhile for AD champs we have terms such as: Tanks/Fighters/Assassins/ADC/Bruiser/Juggernaut to add more of a specification as to what type of champion they are.
Tanks and Juggernauts aren't AD champions, those scale predominantly down the HP itemization line.
Tanks usually scale down the AP/CDR line like mages and supports as well, being more magic and less physical.
Also: in the tank/juggernaut/fighter/bruiser direction, there are a lot of champions that bring a lot of kill potential through hybridized damage that mixes physical, magical, auto-attack, and ability damage together in one large amalgamation of damage.
Prevents them from going wild with damage scaling as AD and AP are often tied to physical and magical damage, respectively. Also prevents otherwise squishy champions like Ahri and LeBlanc from counterbuilding them with 1 item, winning by out-ranging, out-manuvering, and out-tanking the tanks. This in turn allows those tanky DPS champions a clear advantage in defensive counterbuilding and by extension allows them to be tanky and do DPS better than anyone else.
At least in theory - darn that rascal Ekko.
Either way, it's generally safer to consider tanks and tanky fighters as hybrid damage when considering counterbuilding, or just flat out not trying to counterbuild their damage and itemizing against them in other ways, such as the slows of Rylie's or Kingblade so they have issues sitting on your face.
Now I know that certain mages fit into the tank/assassin category but it's just weird how ad champs get so much more specification than ap champs.
You are kind of lumping a lot of champion archetypes into AD that don't really belong there. Marksman is the only archetype that's AD 100% of the time, otherwise there are examples of AP scaling/magic-heavy tanks, supports, fighters, assassins, along with champions that don't really fit in a particular archetype like Kayle.
For that matter: there's also a fair number of hybrid damage champions in the tank, fighter, and assassin catagories.
That said: Fighter and Mage archetypes are really wide-reaching and account for well over half the champion pool in LoL. There are pretty clear differences in the classes, and Riot has even tried breaking them up into smaller groups.
Would be nifty if there were 2 core fighter and mage archetypes to split champions into though. With terms like Marksman, Tank, Assassin, and Support you generally have a good idea of what to expect. Mage and fighter are pretty vauge though.
and 
as just that, assassins and don't believe they belong in the "mage" category, at least traditionally
