I would hope that the majority of voters would see that they are getting better (proportional) representation under this system (even if that representation wouldn't always be as local as it would be for the lucky few districts that aren't gerrymandered into irrelevance in the current system).

In any case, by changing the game theory (removing any incentive to gerrymander districts), my expectation is that in practice no results would get flipped, so no one would experience any bad effect attributed to this system.

It reinforces the idea that parties are more important than anything.

I'm a Democrat mostly, but I might vote for particular Republicans if I feel like they are outstanding individuals with good moral character.

If I cross the isle to vote for John McCain would you take away my McCain vote and give me someone from my party that I didn't want?