The biggest problem is that it's IMPOSSIBLE to prevent your team from feeding.
The first, and most obvious reason, is that there's no way to see the future. No one can know what your team will do and they can't purposefully spread out the feeders. It's possible I could go 50-0-0 for 3 games in a row, trick the system into thinking I'm a LoL god, then trollol the **** out of the next game just because I see you're on my team and I decide to make it interesting.
A few other reasons are as follows:
1. Hard counters. Sometimes you're really good, but you're just put in an impossible situation. If you're playing Vladimir and there's a Fiddles across from you, there's really nothing you can do. He starts draining and you have no hard CC to stop him, and even pooling doesn't break the connection. Plus his stupidly long-range silence to harass you all day long and a fear to boot. So maybe your last three games you played Vlad and went 20-3-7 but this time you got put across from a Fiddles. No matter how many times you play there's a good chance you won't win.
2. League of Legends is very deterministic. This means that the first kill pretty much decides the game. Once you've killed Vladimir once he's out of lane for 20 seconds (giving you time to collect 6 free minion kills) and you gained 300 gold. You also got extra experience. So next time you meet Vladimir he's exactly as strong as the last time you fought, but you have a shiny new blasting rod and you're a level higher. If you thought it was easy to kill him last time you fought, now it's even easier. If you kill him twice, god help him - because at this point you can literally flash under his turret, 2-shot him, and walk away leaving him raging while his team blames him for something he had no power to prevent.
3. Communication is very important in League. When you went 7-7 but your team with 9-40, did you even change lanes to help your team? In many games I've been 4-0 in bottom (killed the ADC and the support twice without either of us dying) when suddenly the enemy mid starts walking down river. The first time we don't expect it and they get two easy kills. The next time we're warded and prepared, but 3v2 is just too much to handle and we may only kill one of them before we're each killed under our turret. Eventually because they worked together they managed to turn the lane around. This is part of the single most important lesson you can learn in League: you WILL, without fail, get trolls and feeders and loser teammates. But you can't help that. You can only change yourself. Ask what you can do better to improve your game next time, because you can NEVER change your teammates.
4. Riot is, understandably and reasonably, out to make money. They make money when people buy champs, and to play ranked you have to buy champs (you need to own at least 16 champions). This means that Riot wants as many people playing this game as possible. Ranking systems which try to weed out bad players will decrease the player pool, reducing revenues for Riot. Sure the 100 people still playing will be loyal and happy, but the thousands upon thousands who had one or two bad games will never buy a Riot product again.
Does Riot try? Yes. Do I think ELO can be improved? HELL yes (if you're interested I'll explain the math for you). But can Riot "magically fix the match-making system to prevent you from ever getting a bad team"? That's just not possible.