In some jurisdictions in the United States, there are significant battles over the payment of private school tuition for minor children as well as the tuition obligations of children who have achieved the age of majority. Some of those battles are legislative as advocates work to install such a requirement, and in other jurisdictions, statutes requiring just that are being challenged.
I've run across this issue from time to time over the years, sometimes in the course of enforcement, sometimes with parents who ask the question at the onset of proceedings regarding custody, support or divorce.
There are two distinctly different issues here. Kentucky statutes only require elementary or secondary private school tuition be included in support calculation only to the extent that there are special circumstances that cannot be met by the public school system, which puts an effective damper on the power of courts to order such payment. On the post-high school expense question, while Kentucky law clearly does not require payment of post-high school expenses outside of a specific agreement to do so, I can see many circumstances where potential enforcement could arise if a family law action took place initially in a state where college expenses are awarded or (in a nightmare scenario of conflicts of law questions) a support case arises in a jurisdiction where college expenses are routinely awarded.
Frankly, my professional opinion is that Kentucky is correct on the subject of child support through college - like the author of the article linked above, I have serious legal objections to the notion that a divorced parent has a differing set of obligations on paying the college expenses of their offspring than a married parent does; as a married father, I am free to decline to pay if I wish, for any reason whatsoever. Approaching the subject on an even more practical level, there appears to be an absence of consideration by awarding jurisdictions of very real objections that a paying parent may have to a chosen field of study, the cost of that course of study, the basic conduct of the beneficiary of the funds, and whether the funds are even designed to reach the recipient (in some states, they simply go to the other parent). This sort of awarding regime deprives the paying parent of agency, often at a time when that parent's earning power is diminishing as the natural byproduct of age; further, as the author of the linked article laments, too many courts are all too generous in awarding college expenses and brushing aside objections and defenses.
This is going to be a major pitfall for lawyers and divorcing parties for years to come, and will only increase in intensity, and it will take quite a bit of skill to navigate through the potential issues.