It is assumed that the government can still prove that you underpaid them if you really didn't pay in full. That's the reason why the job is on you to calculate how much you should pay (the government basically frees itself from it apart from controlling its results). But this is obviously not any more so with Bitcoin since the government can no longer prove or just find out how much you should have paid (at least as long as you stay in Bitcoin entirely and don't cash out)...
This effectively means that the paradigm of self-imposed tax system is trashed
Where I live it doesn't work like that
In respect to individual tax payers (unlike companies), they will have to prove it to the court that you really received that income and didn't pay the tax on it. The civil law says that the burden of proof lies on the side that brings forth claims, that the claimant should prove their claims. And I guess it is pretty much the same in many other countries and jurisdictions as well. You seem to be confusing two separate things. Namely, that you should yourself declare your taxes (for the reason that the tax agencies can in fact prove if you really paid or didn't pay the amount due) with the obligation of actually proving that circumstance in court if they come to think that you underpaid some tax
But back to the point. How can Bitcoin help you in any way in such a situation?