I don’t think that a move to Bitcoin as the world currency necessarily implies that taxation will be gone. The state was perfectly capable of collecting taxes before fiat, be it in mead, furs, wax, wheat, gold, or anything else of value.
As long as the state has monopoly on violence, taxation will be a thing. Or let me rephrase that, whoever has monopoly of violence in a polity (the state, the rebels, the mafia) will collect a form of taxes to finance their operations.
So social programs are fine in a BTC world. As long as whoever has monopoly on violence bothers with them.