Secondly, what makes it much easier to evade taxes by failing to report Bitcoin payments than evade taxes by failing to report cash or check payments? Taxes work because enough companies and individuals pay them voluntarily that the cheaters can be cross-checked into oblivion. I don't see why people would be more likely to cheat if they were transacting in Bitcoin instead of cash.

Cash is pretty anonymous, but also pretty useless for paying people over the internet. Cheques typically leave an audit-friendly paper trail.