It's interesting. When you give $$ for financial aid to a university, you imagine the beneficiaries. When you give $$ to your DC's private school, you actually see the beneficiaries, sometimes day in and day out. That creates a lot more room for resentment -- e.g. I gave to the annual fund so *she* can get a tuition break?!
And I wonder how the formula works. Thinking, for example, about medical care. In less affluent families, the elderly relative who needs FT care may live at home with nursing provided by various family members. By contrast, an affluent family may be able to afford to outsource the care -- e.g. to an expensive assisted living facility. At which point, does the affluent (but cash poor) family get subsidized private school tuition as a result? Who gets told "sorry, you just can't afford private school" and who gets told "well, we'll make it affordable because we can see that your family is dealing with a medical serious medical needs? Basically, it usually takes lots of income or lots of assets to rack up big expenditures. Poorer people are more likely to barter or share or do it themselves or do without rather than spend. Should financial aid be designed to put the educational perks of big wage-earning within reach of unlucky/overburdened big wage-earners or should it be designed to make private schooling available to kids whose parents simply don't have many economic resources (rather than those who expend their resources on other things -- no matter how laudable or necessary)?
Here again, college is different both because the students are older and have more significant track records -- which means both that who deserves what is more a function of individual merit/achievement and that colleges can make predictions about future earning power and/or require the student to share the risk/investment by funding part of his or her education through loans.