Imo they will coexist, as soon as the government finds a way to let the IRS control and monitor the bitcoin transactions

I guess the Federal Reserve and government aren't happy to admit in their economy something they haven't created and can't control so they will work to change that (*cough ethereum *cough). But if bitcoin becomes widely accepted by the citizens they will have to comply to take part in that and collect some taxes better than none at all. The problem with the government is that they are showing through their actions that they seem to assume everyone is a criminal that wants to evade taxes if they use bitcoin so that will lead to the potential ban or restrictions on bitcoin transactions as happened in china. So I have no idea how long it will take until bitcoin is accepted or any other succesor of the coin, one thing if for sure, people want to use cryptocurrencies and any government can't ignore that for long.

P. S. The government of Ukraine is studying to accept bitcoin officially in their banking system. Strangely enough I read that yesterday in coindesk or cointelegraph but haven't found the link today.