One, having everyone in the company able to make executive decisions or at least influence them sounds great, but inevitably more outgoing and charismatic workers will gain influence, even when it's a supposed democracy. You can structure the system to have all the meetings and groups and power structures you want that seem equal on paper, but when someone is popular and outgoing often people will follow with that person. There are going to be people who slip into leadership roles--it's human nature, and trying to minimize that instead of steer it is impractical in my opinion.
The second thing is that having everyone in on the decision making is simply information overload in most cases. I think tasking everyone with being informed and voting on a wide array of things will make them either pretend to know all the issues properly and vote uninformed, or they'll vote the way they see their favoured peers voting. Maybe I'm letting my own experiences cloud my opinion here, since I work at a company that has a fairly flat managerial structure, but it's certainly a problem for me. If they're making executive decisions while not seeing what other ways the company is moving, that seems bad too.
I think there's definitely merit in promoting equality among employees, and it leads to better teamwork. But I just don't think that end of the extreme ever works particularly efficiently, and I think human nature tends to influence most companies toward the more normal business hierarchies.