They will have to radically change their approach to revenue collection, because the only real control they would have is over the acquisition of physical, visible, assets (vehicles, property, any goods crossing a border) and granting of licenses/registrations (to trade, operate a business, deeds, etc).
My take is that there will ultimately be an "official" national government blockchain for the type of transactions that necessitate government involvement (like buying property and registering deeds, or getting a business license), which people will only transfer into when they need to make an "official" transaction, but most day to day income, commerce and wealth will be obscured in decentralised blockchains that government has no control of or insight into.
It spells the end of any kind of wealth tax and probably income tax. Governments will go back to the days of relying on tariffs and fees and duties for their revenues. Which is, funnily enough, exactly how it all used to work before income tax and central banks became a thing in the 20th century. It is also the long term death knell of the banking and monetary system as we know it.
And I have a sneaky feeling that there are secretly a lot of individuals/politicians in governments who have realised that the current debt based monetary system is unsustainable and welcome it as a way out of the ever snowballing mess, which is why governments have so far not been as rabidly anti-blockchain as one might have expected.