Sure, there are always several pathological champions in the league roster. For example, before her rework, Poppy was nerfed into oblivion because of how broken her ult was. Riot nerfed pre-rework Poppy so that she would never show up in pro play until they had time to fix her, and that is O.K.
But for any position there are maybe 20 healthy champions.
There is nothing pathological about having one of {kog, trist, cait, graves, lucian, kallista, draven, varus, ashe, corki, ezreal, jhin, miss fortune, sivir, twitch} as adc. If only 4 are showing up in the LCS, why not tap down base health on the regulars so that pros have a reason to pick other adc's?
There is nothing pathological about having one of {amumu, chogath, mundo, ekko, elise, fiddlesticks, gragas, hecarim, jarvan, jax, kha'zix, kindred, lee sin, maoki, malphite, yi, nautilus, nidalee, nocturne, nunu, olaf, pantheon, rammus, rek'sai, rengar, rumble, sejuani, shaco, shyvanna, skarner, trundle, tryndamer, udyr, vi, voli, zac} show up in the jungle. If only two are showing up in LCS, then nerf the base health of those two after the first game in a series and then maybe we will get some of the others on this list showing up instead.
And so on with the other positions.
The champions that are truly pathological or boring to watch (like warwick) are currently so weak that they would never be the runner up. Nerfing the base health of gragas is not going to break the game. It's not going to cause a pathological champ to show up in the LCS. Instead, it will either cause one other top-tier jungler to be picked instead or the pros will pick gragas anyway because they think he is so strong that he is worth playing with 50 less hp at the outset.
My proposed change will not harm the game; it will increase champion diversity in the pro league.