My mom was a soccer mom (litterally) when I played say 18-8 years ago. Back then minivans weren’t used much… we had a real van, then station wagon, then suberban. Nobody wanted to go home with any parent that had a little two-door toy car - no room for all your friends and they got nit-picky when you tracked dirt in from your cleats.
I don’t know about the US, but in this part of Canada soccer is most certainly NOT an upper-class game in any sense. It’s generally the cheapest and safest team sport kids can participate in. A lot of my teammates came from welfare and immigrant families. Here, hockey is more the upper-class game, probably costing at least 10X more to play (in organized leages)and of course being more dangerous. I don’t think the yearly registration fees for me ever went over $75 for soccer.