The retarded part about this is that crypto currencies are a dime a dozen and the difficulty for making money at it is always at a constant incline, so the more you do it, the less you regularly get, which means you'd have to constantly jump from currency to currency to stay in the lead or try to compete harder for less money than you were getting to start with. Not to mention getting people to take it as payment for shit like infrastructure would be lolno. Not to mention you're dealing in a currency that's not backed by anything, is not held to the same social contract as real cash and if you were clever enough, you could just duplicate your current amount and inflate the shit out of it since it's a purely digital currency. Crypto currencies are turbulent niche play-monies that you can't use in every day life and only works on the internet.
It's also not regulated by the government so whatever happens to it is completely out of their hands and they'd be playing into a foreign economy. Remember what happened to the US economy when Nixon got Saudi Arabia to play with American dollars? It's also worth noting that it's an anonymous currency that can be spent on really illegal things, things that you really don't want to make easier for people hungry for power to do. Not to mention the controversy that would explode from the government forcing you to dedicate CPU space for them, which would be instantly taken, and rightly so, as yet another step in furthering the surveillance state.
This goes without mentioning just how much it would damage the overall economy by forcing ISPs, server hosts and software development companies to purchase more hardware than feasible or necessary to compensate the hemorrhaging caused by the loss of CPU power.
It would be a complete disaster that would demolish the economy for the sake of harvesting a fad currency that could fall through tomorrow.