Will they be able to fully succeed, that is the question.
Succeed in what? Regulating it? They've overstated with KYC in centralized exchanges, wherein most of the users buy and sell from. They already have enough information to control them. Part of the United States' national spending goes straight to Chainalysis.
Fiat forms of money are already being rapidly superseded by the digital version
Whether you pay in cash, via bank account or via PayPal, it's the same currency. In fact, using fiat digitally is traceable. Much better for a government.