Lets face it many people do suck at the game but that doesn't mean that the matchmaker system for making games right now also doesn't suck. The two things are unrelated.
The more potentially damaging reality is that many people do belong at the 1200 rating level sure. However they are constantly beaten down and given horribly unfun games because that is the rating level that all of the trash (future 800 rated people, leavers, feeders, level 20s with 0 games played) is also thrown in at so anyone who is "average" is pretty much guaranteed they will never be able to play fun games.
Where as people above 1200 are able to have fun games because the people in those games deserve to be there. Anyone 1200 or so and below are constantly hit with feeders and leavers and horribles that are on their way down and ruin the game for 9 people. This is the ultimate problem of the system and this is why WoW changed their arena elo system to start at 0 and make you work your way up.
In conclusion ultimately to fix the system the starting elo for all players need to start well below what an average person could be expect to rise to if they play a decent number of games. This however isn't quite enough because they'll still be plagued by the effects of other horribles dragging them down (though the effect should be lessened as if they are good they will easily be able to carry the game as any smurf can tell you). Also there should probably be some way to identify those who are decent and make them more quickly rise up to the average elo level at least. The mysterious part is that this system exists and is in place already for normal games (just ask the smurfs about smurf detection) and yet Riot seems to have forgotten about this problem they already fixed.