One big difference between cycling and other sports (like football) is that the stable factor in cycling aren't the teams, it's the races (and the UCI). There are some older teams like Lotto or Rabobank, but most teams have a short lifespan, especially compared to a sport like football, which has teams that are over a 100 years old.
In a sport like that (football), the teams have a long term interest in the succes of the sport. In cycling, they don't. Guys like Riis and Bruyneel (and I believe Vaughters as well) don't even have a sponsor for next year, if they don't find one, they are out of cycling next year. With this structure, it's almost unavoidable that the teams will allways care about nothing but their short term interests, and therefore you need an organisation like the UCI that stands above the parties, and has that long term perspective. Of course, the UCI are far from perfect, and can be improved upon in many areas, but you need an organisation like that.
The teams complain that the UCI treats them like children, and behave like dictators, true as that may be, you need such a stable factor in the sport. If you give the teams a big input in cycling policy, they could decide on one thing this year (keep the radios), but the next year you could have five new teams, who decide the opposite (ban the radios). The teams have only short term interests, and their composition is far too fluid to give them a big influence on the UCI policy.
Crackpot theory time: what Bruyneel, Riis and Vaughters want is a bigger cut of the television-rights. They are sick of begging sponsors every year for a 1 or 2 year contract, they want to become long term players in cycling. If they get a significant cut of the TV-pie, having a big sponsor is only a secondary source of income, their teams can survive without it. If in such a system they get to decide who has a right to that money, who is part of the in-group, they can set themselves up as the main players in cycling for the next 20 years, without having to worry about those pesky UCI rules, and not having to go on a constant sponsor-hunt, and without the swords of Damocles above their heads that could end their involvement in cycling the moment they fail to find a new sponsor.