TV, if your reasoning is consistent, then I suspect you also believe that 18 year olds should not now be allowed to remain on their parents health insurance plans because they are adults?
Just curious. I think defining adulthood is an interesting legal challenge that today is fraught with inconsistencies.
In my case, I actually did have language in my divorce that specified post-secondary education costs would be shared equally, and that child support would continue "either" until the child was 18, or completed and undergrad degree in the customary amount of time, and I do agree that such language should be there. (it does not seem common here; my divorce was in another country.) I also did not collect alimony, so that did not play in.
So in actual fact, I could have won a court order. I did not pusue it because I did not need to and my general feeling is not unlike yours in that my preference is not to legally compel someone to do something that they are choosing to believe they cannot do, particularly where others are free to choose not to
That scenario notwithstanding, there are two very practical ways this country could prevent the common exploitation of at least the aid that comes from public money, and the known tendency of divorced parents to abdicate the responsibility of reasonable assistance for undergrad.
The first would be a simple change to FAFSA that required the NCP to co-submit -- defined by whether or not there existed a prior legal custody agreement. The second would be a contribution scale with a baseline of state universities that includes the variable of student accomplishment (eg hs gpa of 3.2 or some such). The third would be a legal mechanism to collect said contribution not unlike child support.
It would be pretty simple to devise the regulatory part of it -- eg. Only in play with continuing to post-secondary school within one year, and to end after four. Enforcement of the regulations might pose more of a challenge.
I have a second dog in this race in that like Starbucks, I was once a child from a second middle class family with "new" children where none would pay for school even though I
was a gifted kid who got into a prestigious talent-based program. I could not get aid due to my family's income. I saved a lot, and worked a lot. At one point I dropped out, but
"returned" as an adult. I have no regrets, and am evidence that it's possible to be unstoppable. I was in my 30s when my aggregated student loans were finally retired (and only then through the proceeds of the sale of a house.)
But college costs today are of an order quite different than in 1984

and I think it would be reasonable to protect public dollars for the most-needy by cleaning up a few legal definitions around age.
If a kid can drink at 21, then in theory FAFSAs definition on indpendent should likely be 21, not 24. If a kid can be legally an adult but not drink at 18, then maybe their status as a dependent for education purposes should rightly extend to 21. It might be a truer reflection of how things actually are.
None of the foregoing, however, is meant to suggest that I think it's ok to compel families to pay for private education except by negotiated agreement according to their means.
But I do think clarifying parental responsibility by law with respect to continued education would benefit both bright children and taxpayers and net more efficient use of public funds -- the same way child support laws were meant to reduce the burden of assistive social services.