Are Fighter/Slayers the only counter to Fighter/Tanks?
I've seen many times that League is a sort of rock/paper/scissors game with something resembling the following hierarchy:
Tanks (and Mages late) counter Assassins Assassins counter ADCs (and Mages early) ADCs counter Tanks and outscale Mages
What I don't understand is where the Fighter/Slayer and Fighter/Tank categories fit within the rock/paper/scissor game. A few examples:

The hallmarks of these champs is the following list:
- cc, cc immunity, and/or damage immunity
- very strong chase/engage but can be very difficult to catch
- tank durability or drain tank sustain
- true damage, hybrid damage, or armor shred
- burst damage nukes squishies
- dps shreds tanks and objectives
So the question is, do these subclasses only counter one another? Assuming equal income, what are assassins, mages, and tanks supposed to do against these guys. My experience says you can only run the other way until team fight time, at which point the tank does their best to lock down and peel, the mage uses their full rotation, and the assassin uses their mobility to secure the kill.
The next question is whether the archetype itself is fundamentally flawed. Should durability, burst, dps, cc, and mobility/speed all be packed into the same champ?