The purpose is to keep ranged away from freely harassing as easily, but with how powerful range is in League compared to other games, melee suffer more for it, especially since the game is a lot 'snappier', allowing you to punish melee CSing much more easily.
Another is to prevent easily harassing past them under turret (which held more true in the past). League's gone bonkers in the recent seasons, making this not exactly applicable anymore.
Finally, 'trading stance' is not supposed to be as 'free' in League. In any other MOBA, you have much heavier relative mana costs (as far as damage). Minion block would not be as 'negative' for melees if the costs for harassing via abilities where higher, and if minion aggro (not damage) were much more influential, as in other games when you harass with autos. No matter what, in League, this cannot be fully addressed because manaless champions are a thing.
So there are DEFINITELY solid arguments to get rid of in LoL, or at least alleviating it, but there is definitely a general purpose to minion block. Enemy being removed would actually be healthier than allied, as far as ranged vs melee matchups.