I think it also depends on the parents. Some parents don’t know how to be a successful parent, so they try to gauge it on externals: “my child has this many A’s, this many extracurricular lessons, this many Gap Kids sweaters, this many super-expensive ‘educational’ toys”.
I’m an only child (not by my parents’ choice, maybe that’s why they didn’t spoil me), and while my parents expected me to do as well as I could in school, it was no big deal if my grades weren’t perfect, as long as I was working for them and not just being lazy. I had a dance lesson weekly, but then so did a number of girls that I knew who were from big Catholic families. Mom and Dad wanted nice things for me, but we didn’t have a lot of money, and what we did have went into paying for our two-bedroom house, or for tuition at our parish school.
Mom was a little over-protective (always worried that a sore throat would turn into strep throat, or a cough would be pneumonia), but as they tried for so long to have me and were never able to have another, I can’t really blame her. Even so, I still swung from the monkey bars, played in the dirt, got in scuffles with bullies, etc.
They’ve been pushy in the right ways- making sure I went to college, although it was my choice of where to go and what to study. They were always supportive of me, yet encouraged me to solve problems myself. If I had a problem with a professor or a roommate, they would talk with me and help me figure out what to do, but actually doing it was up to me.
Maybe the problem isn’t so much parents with one or two children, but parents who were only children or one of two themselves. Even 40 years ago, wasn’t the “ideal” nuclear family seen as Mom, Dad, Johnny and Susie? My parents were both from 7-kid families and I think that had a profound effect on how they raised me.