A way to drastically reduce trolling in league

After a particular game with another stupid troll I thought of a solution. First off I'll explain the problem, if you're not interested skip to the solution.

Problem: Trolls are a dime a dozen and banning them does no good. Even if a troll does get banned they just jump back up and get onto another account, therefore there is no action that can actually be taken towards them.

Solution: When a banned account attempts to log in, lock the client for the remainder of the ban time (1 day, 3 days etc....). This wouldn't permanently remove them but at the absolute least they would be forced to re-download the entire client before they could get onto another of their accounts, or wait out the ban (as bans are intended to force them to do). I'm not saying that it would be incredibly easy but it wouldn't be impossible and with what I know about programming, I don't believe that it would be that hard. simply have the code for when a ban kicks a player or stops them from logging, lock the client until a certain date. This could be bypassed a few ways but they would at least be annoying to pybass.