Can you register cars under a company or other shell entity? I feel like the only way to get around this kind of stuff is to have layers of abstraction above your identity.
I've seriously given some thought to do exactly this. It's not particularly difficult. You need a valid business entity (Which you can create for about $100 a year in some states), and a car paid for in cash. Then any LEO running the plates through ALPR will have no idea who identity of the driver is. Literally millions of small business owners do this so it's not particularly unusual.
You can probably use the usual tricks of money launderers to obfuscate the ownership structure of the LLC. eg. you're the beneficial owner but the director is listed as your lawyer.
In Washington State they require an individual to present identification when registering the vehicle (doesn't need to be a WA driver's license though if you're registering the vehicle to a corporation).
State DMVs are ultra-obsessive about tying an individual to every vehicle.