The whole point of cryptocurrencies is that they're decentralized, and can't be controlled by governments. That would defeat the whole point of blockchain surely?
Not necessarily. Lack of centralized trust is just one feature. They have other features like public (but anonymous) ledgers, irreversible transactions, smart contracts, the ability to hold them without a bank account. Features like those could definitely come from a private or central bank.
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.