There's no way a govt can control provate keys if you dont want them to. Hardware wallets are the most obvious, but there are also plenty of web wallets out there that do not store private keys.
As for exchanges, I feel people will gradually start moving to DEXs. The writing is on the wall, with Bitfinex already having created Ethfinex, a hybrid-DEX, and Binance soon to be following suit.
More and more DEXs are popping up (https://github.com/distribuyed/index), and what is most exciting are the protocols behind them: 0x, Swap, Aurora/Snowglobe, etc.