The reason we have a marks(wo)man every game has less to do with them bringing to much, and more with them being able to give something up and be less affected than the other classes.
Marksman, or ranged auto-attack focused champions, are the class that is the most suited for being in a set-up were they have to share experience, but get all the farm. Why?
Because they are ranged and auto-attack focused. (Duh)
Range, in general, is an inherent form of safety - you cannot hurt what you cannot hit. Melees, on the other hand, voluntarily move into range for enemy retaliation, and thus need the extra protection from defensive base stat increases.
Auto-attack damage does scale a lot harder with items than it does with levels - for instance, most marksman get about 40-45 AD total from 17 levels. That's a BF Sword. Ability-focused champions, on the other hand, want those levels to get ranks in their abilities - not only for the extra base damages (compare how much AP you'd need for the same damage increases), but also for the reduced cooldowns (if an ability gets lowered CD/rank). In addition, for mana-based champions, their resource regenerations also heavily scales with levels.
If you want to have another type of champion go botlane, you essentially need someone who either gets full XP (reworked Morde, and we all saw how that turned out) or a very specific kind of mage (low base damage increases, no lowered CD/rank, scaling in some XP-independent way like Cass' passive...).