About the rate of key fragment drops
Make it creep back up after lots of games without getting one.
In theory HTC works really well: people might see 4 chests per month and go "well i should try to keep up with this on all my smurfs too" but then they realize that they need keys too and playing enough to get 4 keys a month on several accounts isn't too feasible. Thus people stick to their main and get the amount of stuff Riot wanted them to have.
In practise, the keys are even more time constrained than the chests, which totally defeats the purpose. You get the first 2 pretty quick and then the odds have dropped so low that you're probably not gonna finish a third before the reset. So the optimal way to free stuff is actually have a whole mess of accounts, play ~10 games on them per month, and easily open 2 chests per account per month. I have most of the stuff I want in this game, but for every person who actually does this theres more smurfs and more free content getting out.
Solution: key drop rates start slightly lower, decrease as usual, but slowly ramp up after many games of not getting a shard.
This way players who play 100 games a month will end up with more keys than players who play 10 games a month, encouraging players to stick to one account, and not getting a key for a whole week doesn't feel as bad.
(Yes, just buying 2 keys per month would solve the problem. This annoys me more because I'm an engineer and it's a dysfunctional systen)