I don't need to register the vehicle if I don't drive it on public property. I don't need to submit my information to the government to buy the vehicle. And I don't need a drivers license on private property either.
Fair enough. So should gun registration be required for it to be carried in public then? So you can buy and keep guns on your private property, but to "operate" it in public you're required to register it. And here in the context of a firearm, operate is carry, not necessarily discharge.
* I don't see how that wouldn't solve any problem with actual gun crime. Cars are required to be registered since they are meaningfully "operated" in public peacefully, guns aren't. For cars this is different because you can see the license plate, whether or not the registration is current, everybody has one... Nobody that wants to remain in good legal standing would drive an unregistered (unlicensed, uninsured...) car on a public road. Outside of concealed carry and a couple political protests, nobody is carrying guns around in public except criminals. Non-criminals shoot their guns on private property like ranges, and transport them in their vehicles on public roads. The latter has never been a problem. And lastly, criminals aren't going to follow silly restrictions like "get your gun registered before you carry it in public to go murder somebody."
* People are paranoid (probably rightfully so) about a gun registration database. This would not only confirm their fears, it wouldn't be useful for combatting crime making the paranoia worse.
If you take a look at CA's gun laws, almost all of them are laughably stupid to the point that they restrict cosmetic features, and where they don't, they don't meaningfully stop somebody from committing a violent offense with a gun. If you understand how guns work you understand this simply: the gun laws in places like CA are meant to stifle gun culture not prevent crime (since they are laughably ineffective) or they are written by people who are very, very, ignorant of how guns actually work. In the latter case, it has the former effect.