In a great many cities, this right is actually restricted. City codes often prohibit parking unregistered/expired vehicles on private property if they're visible.
To put that another way, middle-class and wealthy people don't like to see poor people.
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.
We have bylaw officers in my town. They would be the ones to decide what a junk vehicle is and obviously they are not experts in every area possible so they just use their judgement and make a call. Some other person who applied for a job in my city that my taxes pay gets to determine if my stuff is crap or not. Of course you can always take the city to court if they are acting inappropriately. What criteria do they use? I am going to guess the does the car look like crap test. If so get ride of it. Or how about when did you insure or drive the car last? Not for years well get rid of it. The fact of the matter is, like others have said, no one wants a neighbor that collects a bunch of cars that just rot and look like crap. No one is asking people to get working vehicles and get rid of them. Also, the city gives you plenty of warning. You could show them look the car drives or your intent to fix it. No different then if they determine your yard isn't clean enought....I personally like long grass and bugs, the city not so much. Some person gets to decide is the answer.