Riot asked for feedback or w/e so here is mine. USUALLY this type of social gimmick heavily divides players, especially if its tied to ANY in-game power or in-game 'swag' as we have seen in other games. I doubt anyone is getting max level in two months, but what if it takes year(s) to hit 80? and if not, then what if they add another 50 or so levels later that DO take that long? The social impact is pretty obvious. A sort of standard metric will ALWAYS emerge with super grindy levels, and elitism amongst the highest emerges as well. What I mean is, eventually this notoriously vile and volatile community will be able to point a finger and say a level 40/plat 2 is just some whacko who has not played the game for more than 'x' months.
There is ALWAYS an average player level in this type of thing, and people will check these things using nexus/opgg of course. Someone who has a life or plays other games will fall below the average mark and will eventually face vile remarks such as "i knew we were going to lose when I saw we had a level 35 sona" or maybe if it matches teams with a level 35 on both teams its like "gg you had the better level 35, our shyvana was super bad #matchmaking"
**TL/DR: its probably going to be just as bad, or worse, as knowing someone on your team has played 50+ ranked games and never got past Silver 4.
It reminds me alot of Blade & Soul, where people can merely just see a HM Level 7 and will leave the party. Not because they are too weak gear-wise to do the dungeon, but because they think there is no possible way that a HM7 player is any good. They are assumed to be dead-weight casuals/noobs by the elite. (some grind alot and some whales buy everything that increases XP using $$)**