Melee carries in any other moba tend to have mobility of some sort, and very strong damage steroids in their kit.
They typically end up in a design similar to Yi, which I doubt anyone really wants in this game. But, other mobas have additional checks and balances to keep melees viable as carries that league lacks. For example, BKB and Blink dagger in DotA help a lot for melees to not get chain stunned or kited for ever, and so does the way the very stats work in the game like armor giving agility, or strength giving raw hp depending on the hero type. Stuff like turn rates being in the game also help keep melees from being perma-kited as well. Furthermore, talents in DotA and League help melee heroes adapt and scale in a way that League is sort of missing as well. I don't think this game's really designed for it in its current state. They'l most likely either need to be overloaded to stay viable like Yasuo, or just delete everything once they spike due to the way the game plays out right now. Fundamental item changes would have to be implemented first in the very least, and that'll throw everything else off more than anything.