Return banned bought/botted accounts
Awhile ago Riot had some kind of internal initiative to identify and ban any accounts which had been botted. There were likely various reasons behind this and some of them valid however overall it was very a poor choice.
This hasn't reduced botting at all. It only punished the players who are most committed to League. You can't stop people from wanting to have a smurf, or many smurfs so you may as well embrace it. Because of this I think you should return the accounts to players and start selling accounts in the game store to qualified players (perhaps gating them based off solo q ranked since the people buying these are doing so to smurf in ranked).
Prohibition is ineffective and only exasperates the problem on a number of fronts. The main two being; it gives third party sellers incentive to bot accounts and it puts extremely high skilled players in extremely low skilled games (for those choosing to level an account). Neither is desirable and current state of things dramatically increases the occurrences of both. You're also forgoing a ton of free revenue. Instead it's being collected by people who causing your costs to increase by putting load on your infrastructure in order to produce their product. It just doesn't make any sense.
Lastly, to address the comments. This clearly isn't a popular opinion to have. However, none of these players have any reason to even participate in the discussion. They don't even play ranked. They have no interest in another account because they're not in gold, plat or diamond and looking to be able to play a less serious game with their friends occasionally or something along those lines. Their account suites their very casual, low skill, league needs just fine however, their irrational dislike for the idea of selling accounts isn't any reasonable argument against it. It's just a remark of jealousy. Apparently some people below are offended at how my 3rd or 4th smurf has higher elo than they've ever been able to achieve... Whatever.