We already see this with the banking institutions that grow like barnacles on the side of the blockchain - they track where their customers spend coins, and blacklist the customer if they go to e.g. DNMs. If bitcoin gained wide enough adoption that people could cut out these middle men, the government would have much more incentive to inject itself into the mining process. There is already ample evidence they are doing various things on-chain to track the spending of large/active users, see e.g. https://reddit.com/r/DarkNetMarkets/comments/4fov8h/i_regula...
Edit: FWIW, Bitpay is one of these institutions. Steam doens't accept bitcoin, they accept fiat paid by Bitpay on behalf of someone with bitcoin.