I've done it. I've fixed the smurf problem.
I had this idea in reply to someone's "what should they do about it?" comment in another thread. It's so simple. Well I mean it's simple in theory.
Every computer that downloads League must download a software key with it. That key allows only one account to access League. Multiple accounts in the house? You'll either have to share or use different PCs. This is the price of billing yourself as a serious competitive game in which every player in the ranked system could theoretically rise to the ranks of a pro.
If someone cracks the key for multiple accounts, lifetime ban and a report to their country's authorities for technically hacking a company's (Riot's) security software. If someone wants to buy multiple PCs to get past the key restriction, well, they really want to smurf and they've literally spent money to do it, so they're probably not quite sane. At least the vast majority will think twice before having to shell out actual money.
It's not fooproof, but nothing is. There isn't a 100% flawless way to prevent anyone from doing anything, but this would be more effective than just shrugging and letting people make however many accounts they want.