The thing is, stuff like going for the jugular, getting a headshot, striking a vital, etc. all imply very precise, intentional strikes, and so should not be dependent on randomness. League is a game about exceptional champions expressing their unique skills, so unless there's a champion who specifically revolves around luck (Twisted Fate, maybe?), players shouldn't be dealing tons of extra damage just because in-game they just randomly happened to hit a weak spot. That implies clumsiness, and has no real place in a game that has more than enough systems to express skills.
At its core, a critical strike is just bonus damage. It's the reason why certain spells have critical damage indicators when they're empowered (e.g. hitting a single target with a Karthus Q, or using E on a frozen target as Anivia), and why Randuin's Omen reduces even those effects (EDIT: Randuin's no longer reduces spell crits, ty for the correction Champion Skin). Whereas in pen-and-paper RPGs the only way of allowing this to happen was through dice rolls, League is a game with so much interactivity that there's absolutely no need for RNG to determine the damage you deal. In fact, it doesn't even need to be a specific mechanic, as bonus damage or empowered effects are good enough to describe how abilities and attacks can function under special circumstances. However, I very much agree that the current bursty nature of crit would be a better fit for assassins than for marksmen, as the former could use a lot of flat damage in one go to burst down squishies, whereas the latter should be focused on dealing with tanks, and currently are far too bursty due to their crit.