The axiom upon which this reasoning is based ("everything needs to be designed/balanced around a constant") doesn't really hold up when you look at other MOBAs, which don't require a character or class of characters to be mandatory in order to do their balance. Furthermore, marksmen aren't really much more constant than other champions, as in spite of their reliability and presence in the game, they're still subject to many changes in their balance and itemization.
I also feel the above reasoning mostly tries to argue the premise from the conclusion, by inferring intended rules from the current state of the game (e.g. "tanks peel for ADCs"/"Juggernauts kill ADCs" and all that). Really, tanks should be peeling for their squishy teammates, and engaging for the team's damage-dealers, supports should be assisting their team as a whole, and juggernauts shouldn't have their worth determined by their ability to make a beeline for the ADC, yet the reason why that isn't the case is because the meta has become increasingly distorted around the marksman over time (and the marksman specifically, as ADC also implies melee carries like Yasuo or Master Yi, who are completely out of this picture).
This was mentioned a long time ago in a design discussion, but class relationships at their baseline are cyclical, not centered around a particular class: marksmen are strong against fighters and tanks, fighters are strong against tanks and assassins, tanks are strong against assassins and mages, assassins are strong against mages and marksmen, mages are strong against marksmen and fighters, and supports are strong with allies and weak alone. Effectively, you could easily center the meta around fighters by significantly buffing them and giving them generous stats on items, as was the case in Season 2, or even around supports, whose unique dynamic and priority target status in most games would allow them to have balance centered around them without negatively affecting other classes (plus they're also just as mandatory to the game as marksmen right now). Marksmen may be very consistent in how they function, but that in itself is not a good thing in a design environment where champions are frequently given entire reworks for being too reliable.
My hypothesis on the mandatory status of marksmen is that the class initially fit rather well in a positional meta that had formed around Dragon control, and then Riot balanced the class around being the game's designated carry, due to carrying over Dota's focus on autoattack damage scaling, leading to them becoming mandatory as long as matches had a late game. When Preseason 6 hit and shortened game durations, marksmen also had their early game buffed and their scaling accelerated via cost reductions and stat buffs to their items, leading to them becoming not only mandatory, but also dominant. Alongside this, changes to itemization and design at large, particularly related to supports, further centered the game's design space around marksmen, with non-marksman champions essentially being balanced or even designed around their ability to affect the marksman. It's a situation that can be amended, but that is difficult to realize when you're immersed in a space that feels like the game cannot function without marksmen, simply because they've been a constant for so long.
