Cash-only for everything is just about feasible, if you accept the extra costs of theft prevention. But bitcoin? Bitcoin is ridiculously traceable. Every transaction is public. Make one opsec mistake and everything is exposed.

You're also assuming that the government would sit still in the face of a serious erosion of the tax base, and not crack down on it. The US is bad enough with its arbitary seizures of cash, let's not destabilise the situation further.