tl;dr: Even if you only use spray wax after a wash, it's better than nothing.
It depends on where you live, what kind of driving you do and how you generally maintain your car.
The short answer is that waxing a car puts a sacrificial layer on top of the clear coat which sits on top of the paint (assuming that you have a generally standard paint job). That means that any contaminants (e.g., dust, bird crap, acid rain, etc.) has to get through the wax before it can start bothering your clear coat and then get to your paint.
The rust question is rarely tied directly to waxing, though. For example, when I think of your example cars, I think of rust around the door edges. That was often a case of bad drainage or bad paint at those seams and edges, not a question of wax.
That said, the process of washing and waxing the car generally means that you're spending time going over the finish and looking for problem spots before they get worse. The chances are higher that you'll spot an area that needs touch-up paint before it becomes a big problem if you're already looking at the cat, after all.
Besides, even cheap cars are expensive. It's worth a little time to inspect and maintain your investment. Even if you only use spray wax after a wash, it's better than nothing.
EDIT: responding to the specific question about rust:
Any sacrificial layer acts as a barrier between the ruster (the water) and the rustee (the metal). In addition, it acts as a barrier between the metal and a corrosion-enhancer like road salt. If the salt can get to the metal, it encourages water to concentrate and to corrode the metal. Normally, you have paint and clear coat between the metal and the world.
However, I drive on roads in the real world and, sadly, my paint hasn't remained pristine and perfect.
Even if you have a deep scratch or pit (say from a stone thrown by the truck in front of you) that actually pierces the paint, wax can sit in the scratch and act as a barrier even without paint. This is especially important if you aren't microscopically inspecting your paint all the time (I certainly don't).
Here's what I do when I don't feel like waxing: pour a bit of liquid wax into the bucket before you wash the car. You'll get a layer on the car without a lot of hassle.