1. It allows for a false sense of skill for lower ELO players. It really is VERY easy to pick 3-4 champions that have synergy and just abuse that fact to take down someone 5+ divisions above you on the ladder. It doesn't mean you are better, it means that you brought friends. It's pretty much the same thing as when 4 gang members beat up on one helpless dude, it doesn't make them tough or even good fighters.
2. It is driving away players. Eventually DQ will cause Queue times to go so high that even people who enjoy it will suffer ill effects from it. The longer it is active, the less solo players will play, until eventually they all go away and non premade games of league are a thing of the past, as well as starting a match in less than 30-45 minutes.
3. It is allowing people to climb well beyond where they belong on the ladder. Making the competitive ladder essentially no different than playing blind pick.
4. It is creating an environment where people will not want to play unless they have all of their buddies online, which will eventually lead to a smaller player base as people get tired of sitting around waiting for a group. (think world of warcraft before they put in raid finder) Sure, you can que up with randoms, but people will get really tired of doing so as they will be facing a premade most of the time.
5. Any real, competitive, gamer is turned off by this. The only people who would support such a system are those who do not belong at the top and used unsavory means to get there. You are condoning cheating to win, and you know it riot. Karma is a bitch, and she will be paying you a visit.
6. If people want to play with friends, there were already plenty of options to do so. This is just an effort to make bad players feel better about being bad and will result in lost business for riot. Ranked should be about determining individual skill across many categories, not just how well you can assemble a premade. Sure, teamwork should be PART of that but seriously basing competitive ladder on anything besides your solo performance is a joke.
TL DR: DQ is horrible and there are plenty of reasons why. Taking out duo queue and just having it be purely solo queue is a much better idea.