Not necessarily. Right now cash is anonymous. It changes hands without any record. It has no provenance. And is a centralized currency. There was a joke at the top of the crypto reddit a few days ago about how cash is just more convenient than bitcoin for ordering a pizza. It doesn't have to be government but I would like to see a trusted owner actually own the governance of a crypto currency. Right now it is way too wild west to instill a lot of confidence. Which is great way to make a lot of money quickly. But over the long term I can see a lot of issues coming up.
Maybe this is the reason why most governments would like to ban cash? Or at least restrict the amounts being processed by one entity. It's all about control.