I think we must first look at Monero and how the government reacted on its privacy feature.  Then we can apply those reactions to Bitcoin when Bitcoin (hypothetically) became privacy coins like Monero.
We can set this article from Binance.com titled: why monero being delisted? is there any xmr alternative?

In the article it gives a description of Monero and the reason why Monero is getting delisted.  It stated that the major reason why Monero is getting delisted is due to regulatory pressure.  Since Monero hides traces of transactions, government and financial regulators are cracking Monero.  

Another reason is the Anti-Money Laundering concerns.  Since Monero transactions can't be traced, the Authorities are concerned about the cryptocurrency being used for illegal purposes thus the reason for the delisting.  In addition Binance.com also stated the following reason for delisting Monero:

Exchange Liability
Lack of Transparency
Geopolitical Influence

Details can be read on the link given above.

Thus, applying these situation to Bitcoin when it became anonymous like Monero, we can say that the government and financial regulators who are friendly with Bitcoin will turn 180 degree implementing regulations that is implemented to privacy coins like Monero.

Bitcoin will be cracked down and will be delisted from exchanges.  The government friendly stance will become hostile and possibly implement ban on Bitcoin just like what they did with Monero.