The ability of lawmakers to caucus around issues, rather than party, would be greatly enhanced, and even demanded by the public. Even voting would change, as candidates for federal office would no longer run as Democrats, Republicans, Greens, or Libertarians. They’d all be Independents, espousing whatever views attracted the most voters.
I think voters would also keep a better eye on their reps after they arrived in Washington, as it would no longer be assumed that your rep would just vote the party line. Folks would have to pay closer attention to what their reps were doing, to see if they got what they voted for.
Your two paragraphs above are reasons enough to abandon the parties. Even if alliances remained. Because it would change PEOPLE’S PERCEPTIONS both at the state level (in CA half the people wouldn’t feel disenfranchised from moment one like we do now) and, as you say, about their rep in DC. (I never pick up a phone to call my reps. It would be the same futility as asking the ATM to give me $1mil in cash.)
Anything that gives people the motivation to stay politically involved and feel like there is a chance for a government by and for us is a step in the right direction.
We’ll never get rid of political factions and labels, even with a constitutional amendment forbidding affiliation with political parties at the federal level, but I do feel that adopting such an amendment would encourage more ‘truth in advertising’ among the elected class.
It would be a lot harder for someone like Olympia Snowe to go to Congress and claim to be a Republican, while voting with the Dems timed and time again. Aspiring office holders would have to run on a liberal or conservative platform, then stick to that, if they hoped to be re-elected.