I mean, that is a nice idea - but how does that actually work?
Where I work currently pays me in federal reserve points. Does this new Constitutional government accept payment in taxes for federal reserve points? Where does the capital means to pay in the exchange currency, whatever it may be, come from?
Where does the means for the new government to pay military, for example, come from?
There are whole hosts of legal questions regarding contracts, ownership, etc.
Further, the legitimacy aspect. There are a lot of people who are currently benefitting from their position within the corrupt system who have no reason to accept the transition to a new system. You have the complexity of trying to explain this to people, why they would trust the ones giving that explanation, etc.
This is even more sensational than some system whereby mass arrests are done by the military with an exposition dump by them about why it's totally legitimate.