Not American, but

1. I don't think Texas was around during the Tea Party, and

2. Property is also a right, so this is just about how much privacy you are willing to sacrifice for how much property.

I've yet to hear a convincing connection between driving down a public road and having privacy - in fact, the outside of a registered motor vehicle on a public road is about as non-private as you can expect.

You already have a unique plate tied to the registered owner of the car, and a range of court cases have held you can be stopped, ordered out of the car, questioned (by both police and immigration enforcement), etc.