Bitcoin cannot "challenge" the "dominance" of the US dollar. Cryptocurrencies are way too unstable to be useful, are useless as capital in building and operating a business, and lack any sort of protections or the possibility of redress against fraudulent activities. Cryptocurrency transactions are outrageously expensive and are economically feasible today only because the mining process subsidizes the transaction costs. Once the supply of new coins diminishes those costs will be passed on to the persons trading the coins and for transactions of moderate size the transaction cost will exceed the amount being transferred.
The only concern that the government has about bitcoin (and it is a legitimate concern) is that its principal use (after speculation) is tax evasion and black market activity including kidnapping, digital extortion, human trafficking, and the buying and selling of contraband. The popular advice to "hold on for dear life" exemplifies the fact that the vast majority of coins are not being circulated; they are just being held for speculation. Currency by definition must circulate or it is not currency at all. Crypto does not circulate because it is too volatile.