No, thats not how that works. The exact banker backed things would just switch over, they will leverage their infinite wealth to buy up the coins on mass if they want to. And when the majority hqs a trackable currency do you really expect the gov to just roll over and stop? They will weaponize it. They will attempt to build a system for precise regulation and for example demand all wallets be registered and if you transfer to an unregistered wallet they could come after you.
If everyone used a privacy coin they could also attempt to do so, but with the privacy coin obfuscating the transactions thats not going to go very far.
I want you to take a look at what happened with the canadian trucker protests funding for reference.