Being required to wear a real-name badge in a public place is much more unsettling.
Given it's impact on day to day life, perhaps it is time to change that.
If your unregistered car is not in disrepair and you aren't storing multiple cars in your front yard, you're very unlikely to be cited.
I just looked up my town ordinance and it only applies to "junk motor vehicles."
The way most places I'm aware of structure it is vehicles that don't have current registration or that can't move under their own power. That's potentially more broad than "junk" but also a more objective standard.
This sort of law can have a severe impact on poor people. Imagine you're barely getting by, then your car breaks down. This is not unlikely because as you're barely getting by, you have an older car and you're not having it maintained professionally on a rigorous schedule. It's going to be a while before you can afford the parts - let's say a "new" transmission from a junkyard. It sure would help if you didn't have to pay $100/month to keep insurance on it though. Of course, that means you have to turn in the license plate, or they'll suspend your driver's license (in certain jurisdictions).
A lot of people have to sell their car for scrap in this situation, which does not give them anywhere near enough to replace it with something reliable.
And just exactly who determines this "junk" status?
Snark aside, law isn't code and the "reasonable person" test works well in most cases.