My 2 honest cents on this, due to the brilliant question you posed.
The short term answer is yes, they will stop overspending for a short period of time. The mid and long term answer is no, they will not.
All you have to do is look at the history of gold. 1971. That will happen again, especially if people don’t put a stop to it. Education is key, but it is not bullet proof.
To answer the second question: they will do the same thing they did for gold: make it a standard, realizing they can’t print more, they will confiscate bitcoin from everyone, then re issuing fiat currency once again. This happened so many times throughout history with gold. I’m damn sure they will do the same with bitcoin.
The game changes because, if many people starts using bitcoin as their standard (even if becomes “illegal”), the state will collapse. The state will be forced to treat citizens as clients instead of slaves.
This book is crazy scary and, even though it was released in 1997, it missed a small margin of what will happen in our currrent years.
The Sovereign Individual: Mastering the Transition to the Information Age https://www.amazon.de/dp/0684832720/ref=cm_sw_r_cp_apip_93bx8bFQQLzcr