After a particularly annoying game where the rest of my team were farming bots, I had a thought. Before you get mad and think this idea won't work or it's stupid, it has worked on many games.
But my suggestion is simple: make it so you can pay to get your account to level 30 (or near that).
If done right this will take the bottom out of the market for selling accounts and give players a legitimate way to pay to get up to 30. They'd still have to buy all their runes and champions but it means they have a legitimate way to do this. Also I don't class this as P2W, more P4C (pay for convenience) as they're not getting any real advantage, if anything they'd have less ip and champs than if they just leveled their account on their own.
Like I said, many games do things like this because of bots/account selling issues and it works well and make it easier for people make smurfs or just a new account for a new server. Sure more smurfs can be bad but I believe that the bot problem is worse and I'm sure Riot can monitor the situation and I'm sure the possitive far out weigh the negitives.
The second question is cost. I actually checked and a quick google search tells me you can get a lvl 30 account for $30US, now this is againist Riot's ToS and so when it's found out, it'll the account get permabanned. So you'd be down $30 (and up some nice malware probs) My idea is for it to cost 6000rp so about $45US ($60AUS) but have it come with some cheap champs (Garen, Annie, Ashe, etc) and a generous IP boost. (Maybe even some rune pages or a skin thrown in too). Now some people might call that steep but when you consider it takes a long while to level up an account to 30, particularly if you have work/school it works out if you have the cash and play often enough in your spare time.
There are many haters to systems like this, saying it cheapens the game and makes it easier for toxic players to just get another account. That's already happening just with the added pain of farming bots everywhere. Also it can be seen as greedy for Riot to charge for this, but it's not forcing you to buy it, it'll just be there for the % of people who just want to be at level 30 and don't want to grind for it.