Your numbers are arbitrary. I have put some thought in this, win totals does not equal ability, even the worst trolls end up with wins, and with enough time and enough games they'll hit 300. ADC players will hit your numbers before most other players, support last, and really support is a position that is overlooked. They initiate, cc, heal, etc. so that the carries win games. Even with assists they won't have nearly as many monsters and minions kills since they let their ADC get last hits. So at 50 minion kills per game that's 1600 games. Even 100 minions is 800 games which is unrealistic.
Something should happen, but don't we have a tribunal for this? Doesn't the ELO help remove these players? I believe dodging is actually what keeps these players a problem. You dodge them until they get what they want and then they play. If you don't dodge they end up losing or being reported.
Yes your ELO takes a temporary hit but if you belong at a certain ELO you'll move right back up the next game, they won't because the next round they'll lose again, unless someone dodges over and over until the trolls get what they want. Call their bluff.
But as for minimum requirements, yes. 16 champs, full rune pages and full masteries should be their only options to choose from. But if someone with only 5 runes is in your ELO then I think we should discuss other problems, such as how they achieved your ELO and you aren't higher to start. Lolking has your solo ELO at 1194, 177 wins and 177 losses, not sure if this is accurate, perhaps this is your frustration because the new people start with 1200.
I'm an analyst, actually an accounting analyst, so I'll try to do my best here and will play the Devil's advocate. So if you're playing with a bunch of new people at the 1200 ELO placement, then it could be that you are getting a lot of new players to the ranked queue and therefore have new people on your team. This is your frustration from what I'm reading. However, you should have (law of large numbers) a larger number of opponents that are new players (25% more to be exact). Reason is that you, in theory, are not new (354 games ranked solo 5v5), you have 4 teammates that can be new and 5 opponents. So according to the law of large numbers, you should be able to differentiate yourself from the group, because your ability should slowly sway your teams to more victories than losses. Also, if you had a good duo then there should be 33% more newbies on the opposing team.
Conclusion is, that you either need a better duo, Riot has singled you out to have all newbies and the opposing team all ranked studs because odds and chance eliminate the possibility that you only get bad teammates and awesome opponents, or that for some reason you belong in the 1200 range.
So if Riot implements some sort of threshold for new players, then it stands to reason you'd be playing tougher opponents, would that truly help your ELO move up?