No. Bitcoin should work if miners are merely individually rational, i.e. they try to maximize their pay-offs without colluding with others.

And it still would. Non-collusive miners cast votes based on the outcome of their own attempts to double spend. If enough agree then they all agree that the vote is binding.

I guess word "honest" might have different meanings, that can be a source of confusing.

1. Honest -- not trying to destroy bitcoin
2. Honest -- following rules which are not required by the protocol

I'm using it in the same sense Satoshi used it. Honest miners work to prevent double spends. That's the entire justification for their existence. Miners that are deliberately trying to double spend are worse than useless.