I don't think Riot realizes the real problem with Botrk

Isn't the item. It's literally just all the damn buffs they did to everything it does. The healing on passive was added, minions were given less armor for more hp, the build path was cleaned up (and no cost increase), the damage was pushed towards AAs instead of burst (so people who pump out more AAs synergize with it better than those that have an ability focus), the passive damage was even given a minimum.

I mean when you just keep changing the item and the way it builds how do you not expect it to end up broken on people who you pushed it towards.

The way to nerf Botrk is to push the gold cost to 3500 and half the amount of healing on the passive on creeps bigger window to bully people reliant on it (sorry Jax, but this puts Vayne back in place). Also it would be nice if it was the only thing the passive healed the user for is the amount of lifesteal on BotRK instead of total lifesteal.