Not at all, they'd simply have to adjust. Since it would be easier for people to hide income, the government would have to drop income tax (which is unjust anyway) and increase other taxes like VAT. If there was no fiat (which I doubt is ever going to happen) and the world used purely cryptocurrencies, the governments would have to gather money by taxing sales and property. It used to be done this way and is still being done all around the world.
I think I'd rather pay more for every product in the store, or for owning real estate, than being robbed of a percentage of my income each month.