It seems possible that they could do that. I don't think the political will will arise unless Bitcoin poses a meaningful threat to the stability of government. So far, that isn't the case: they will continue to collect taxes on the trade of the asset and work on the interaction points to handle dishonesty and lack of reporting.

It might be different in a world where people can do the majority of their day-to-day transactions in Bitcoin, but still, remember that currently, Bitcoin is in no way anonymous, the transaction history is fully public and mostly tractable.