There's no reason why funding higher education has to be all or nothing, either. While you don't want to see young people start out their lives mired in crushing debt they will struggle for decades to dig out from under, I do think it's better if kids have at least some skin in the game. You tend to appreciate something more if you work for it versus if it's just handed to you as an expectation that you can take for granted. And a college education is still a privilege and something that should be earned, not a birthright.
My goal is to fund half of my niece's and nephew's college expenses at one of our state U's. They can make up the difference via working PT like I did in college, or taking out loans, or getting money from their parents, or being good students and earning scholarships, or any other way they choose. If they want to go to Stanford, they will still get the exact same amount of cash from Aunt L (me) as they would have gotten had they attended the state U, and again, it will be their responsibility to make up the difference. Obviously in this case, the difference will simply be a lot higher.
It ultimately depends on what they value in a college education. I am a very satisfied state U grad myself, and I personally do not feel that paying for private school is worth the cost differential. So I am not going to subsidize that. But if they feel differently, that's their business. It's their money, and they are free to make their own decisions regarding the value of attending private schools (and live with the financial consequences of those decisions).