One of the major issues with our current system of government is that the country is controlled by one of two parties all the time, and these parties are constantly butting heads. Each side always wants to get their way and often will automatically nay-say anything the other party says in order to get their way, not bothering to ask the people they represent what they actually want.
If more than half of Congress was composed of independent members, no one party could ever have a majority, allowing the issue, not the party presenting it, to become the actual point of contention.