I am sure governments are not making such groups of anonymous and non-anonymous cryptos. As long the cryptos are decentralized, all are same to any government. So if a government wants to ban crypto currency, they will ban it all and not as per the group made by you. Governments will usually want to control their own economy and since cryptos are decentralized, they can't control them. So they will ban all crypto if they want to regardless of anonymity.
Also the price will have a hit if a big country like India, US, China, South Korea bans cryptos completely. The majority of the crypto users are from these countries and if these governments ban it, we will see a drastic drop in the market cap as well as in the price. So it is going to affect big time.
Let´s say that a regulation requires communication of large capital movements in crypto. How would you be able to enforce that on privacy oriented coins? I think that would need to be addressed.
If the governments were to have their way, a blanket ban on all cryptocurrencies would have been their best bet, because the duo of decentralization and anonymity are unarguably, huge threat to the control and manipulations governance feeds and thrives on.
Apparently, the countries, so far attempting to ban Bitcoin and other cryptocurrencies are obviously not among the power blocks - they'll however sooner than later retrace their steps back to the doors of regulation. The advanced countries would rather not encourage the massive switch over and adoption of those coins aimed at enhancing privacy, so they're just okay with regulation, knowing that the move is inevitable in the case of a ban on cryptocurrencies.
