I grew up middle class - small military town in the middle of nowhere - and both my brother and I got cars when we got our license. They weren't expensive or fancy (actually, mine was quite pretty, just old with a half-working transmission), but they got us from point A to point B.
In fact, the badness of the vehicles was kind of what made them fun. My brother LOVED ugly cars. His first vehicle, a pickup truck, was so battered that when he got in a couple fender benders over the years, you couldn't tell where the new dents were, because they blended in with the old ones.
He eventually replaced it with a purchase that was my idea. There was this rusty brown station wagon I kept seeing around town with $300 soaped in the window. At that price, you'd think it wouldn't even run, but I kept seeing it in different places, so clearly it was mobile, and I convinced my folks to check it out.
The bottom half of the doors were rusting off and there were bullet holes in the windshield (the shots had been fired from inside the vehicle), but it did indeed run. We replaced the tires and got a new windshield, and that was the vehicle my brother took to college, where his classmates promptly dubbed it the "lepermobile." Got about two years of good use out of it before it finally died.
There weren't any real "rich kids" in my town (closest were the children of doctors/dentists, which is money, but not MONEY, as I came to learn when I was older), but lots of kids had cars. The student parking lot at the high school was well-populated.
In a small town with one public bus route and a total of two buses (one traveled clockwise, one widdershins, on the same big circuit that took about 3 1/2 hours to complete), a car was a necessity for anyone who had a job or needed to go anywhere beyond school and back (or to school, for the ranch kids who lived beyond the range of the school bus routes).