Hmm...I could try something like that...I doubt it'd get anywhere though. Minions are definitely op, don't get me wrong, but that's actually exactly where the issue lies. It'd be pretty difficult to make a concept that could turncoat enemy minions without it destroying the entire game in multiple ways.
First and formost isn't what you think: it's actually the gold and exp factor - you turncoat a wave of minions, you're actually gifting your opponents exp and gold that your team would otherwise claim, as long as they're around to claim it. Not only does this naturally put you behind, but because this style of champion would more than likely be a support or possibly some really strange type of support-jungler similar to Ivern, you're giving away exp and gold that would belong to your teammates, which is 500iq trolling at its finest.
NEXT is the obvious - the siege potential of this champion would be stronger than proxy singed, with even less effort involved. Imagine you take a champion top that can turncoat minion waves while theres a 4v5 teamfight in the works at mid or bot...you turncoat minion waves as they come, and suddenly (almost invisibly) there's this MASSIVE creep wave that make URF anivia's minion corral strategy look tiny, and it'll probably take no less than 2 champs to handle it, while you walk away after changing 2-3 enemy waves without ever even coming into contact with the enemy. Mind you, this is balanced in part by the fact that you just gave them 2-3 waves worth of extra gold that was meant for your team...but you more than likely took at least two towers without putting yourself in any real danger.
Lastly, there's the late game factor. You're 3 inhibs down, supers all up in your base, every wave is converged, attempting to take your base...boop, you now have this massive wave of minions from all 3 lanes, including super minions, and you can keep doing this to hold a siege for days...at least until someone dives you.
