From what I've seen, once parties are dropped from the ballot (it's common to have positions where party isn't listed) people seem to stop caring about them. I've seen hyperpartisan areas where people will never vote for party B over party A when party affiliation is listed on the ballot, but when it's not listed they end up happily vote for someone from party B over A. Removing parties from voting would make it less likely that so many issues break down among strict partisan lines, and would make compromise much more likely because not every piece of policy would be tied to a political identity. Factions would still exist, but they would be much more fluid and adaptable.
