first why would anyone want to conceal the fact that he bought a car! as far as legal things go, nobody wants that kind of privacy really except the criminals.
second is that i feel like you are taking steps backwards. with bitcoin you send the coins so to speak to another key that the other person only controls. when you are not sending on-chain and transferring the wallet you are opening ways for lots of fraud. and why would you even use bitcoin! use cash if you are that concerned.
Regarding privacy, governments are made up of people. So, it is people who say what is fraud and what is not.
Let the world watch what you do in your bedroom, right? I want privacy.
In the States, it is not required that you have a drivers license, or a license on your car. Study it. Government doesn't advertise it, but they will agree with this.