The benefit is a more free society and less systemic risk.

It doesn't benefit the sovereign authority directly, but neither does freedom of speech, religion, etc.

The gold standard, in the same way, formerly removed much of the ability to conduct monetary policy, and it was supplanted because it turned out that counter-cyclical policy was very useful.

Cryptocurrency is similar except that it wastes a lot more energy to accomplish the same thing.

The government, of course, retains unlimited power to tax, so the ability to fund whatever it wants is retained in all cases.

"Cryptocurrency is similar except that it wastes a lot more energy to accomplish the same thing."

Out of curiosity, what's the carbon footprint of bitcoin mining as compared to gold mining (and then parking the gold in a depository vault)?

Gold mining is ecologically destructive, but varies based on the form. When gold becomes absurdly expensive, as would happen under a renewed gold standard, it would be very likely that the proposals to mine the sea floor would be pursued, and could have major ecological damage. As for carbon footprint, specifically, I don't know.

Thankfully, USD is not based on gold at all.