Don't all exchanges ask for a picture ID, SS# and other private info to open an account? That's not anonymous.
There is no escaping big brother. Governments can do anything and enact any law it wants to. They can ban all cryptos outright, or ban transfers of cash from crypto exchanges into bank accounts. If they don't want you to use something, you won't. Once "Fedcoin" is mandated by law, all other cryptos will most likely be deemed illegal.
I've exchanged thousands p2p, no exchange needed. Some through exchanges, they were taxed, but not an issue also, keeping in mind all other upsides. And decentralised exchanges will enable doing the same without even meeting and no ID's, nothing. Just read on the technology, you have quite a wrong idea of how all this works.
And no, government can NOT ban anything in this case, unless they ban internet, that's the whole idea. There is nothing to ban to begin with, you can ban even internet, and it'd be possible to transfer wealth in that way using a phone text message still (at the wors case scenario) if really needed. As long as PEOPLE will consider it having a value, it will have a value, no matter the "official" stance of a government. You can ban gold, but you will hardly stop people from trading it for goods/currency/etc, it is tenfold more difficult with crypto.
With anonymity oriented cryptos, there is inherently no way to track anything at all, but bitcoin can be anonymus if you want to, no doubt about that.
This is a new era, new kind of wealth, a way of transferring it and it is here to stay.