I think it's important for parents to pay for post-secondary education, at least for one degree, if they have the financial capacity to do so.
My parents paid for my university degree, but they also made me get a job, as they didn't pay for my books, and only gave me a stipend to cover some of rent/food, but not all.
End result: I got my degree without having any debt.
That's the real issue: if the parents are physically capable of paying for an undergraduate degree, then the result is that their kid doesn't have m/any student loans, and so the ground they're on when they graduate is so much firmer.
I seem to remember my parents saying that they'd only pay for the first degree, which is fair. I stopped after my undergrad, but my sister got a Masters and went to teacher's college, and I don't think they helped with that. Which is fair. She was on her own two feet by then.
I also remember my parents saying that they'd only pay if we went to school right away, rather than doing a travel year. My sister wanted to travel (and she wanted to take the tuition money for that year and use it to fund her travel), and my parents said that if she wasn't in school in September, they would use the tuition money for that year to pay down their mortgage. That made her think twice lol.
My wife's parents paid for everything, and so she could devote all her attention to studying, but it was well within their means (he was the chief financial officer for a multinational), so why not, right?
Of course, I'm Canadian, and our universities are heavily subsidized. My tuition was about $4,500-5,000 per year, so that's easier for a parent to save for over the course of the child's first 18 years. (I understand it's a lot higher in the US?)