I wouldn’t exactly put it that way, but it is a logical consequence of a couple things that I think are understandable.
The first thing is that it takes a certain amount of money for a family to just cover basic needs like food, shelter, clothing, necessary work expenses, health care, and so on. A basic education could even be considered on this list, but I would suggest that only applies to community college, or maybe an in-state residential college at whatever your state will charge you.
When it comes to paying more for a private college because it is seen as superior to such a basic public college education, that is properly seen as a type of luxury spending (not pejoratively, just definitionally). And luxury spending typically comes out of whatever you have in addition to the basic financial resources. And the details differ, but at a high level these colleges are basically looking for you to pay a certain percentage of your available luxury money on college.
OK, so suppose you only have what they see as the basic financial resources (or less). Then they will more or less not look for you to pay anything. Suppose you have a little luxury money, but not too much (as they see it). They might look for you to pay a percentage of that, but since you don’t have much total luxury money, it won’t be much, either gross or (likely) as a percentage of total income. Suppose, though, you have a decent amount of luxury money, but not so much you can afford the whole thing. Then you will have to pay more, but not full pay.
This continues up to the point you have enough luxury money, as they see it, to be full pay. At that point the percentage of your total income that is luxury income as they see it is likely to be relatively high (although it depends on your assets, but we can hold that aside for the purposes of this conversation). So their assessment of your luxury income will also be relatively high as a percentage of your total income.
OK, so that’s the first thing. The farther above what they see as an unassessable basic level of financial resources you get, likely the higher that assessment of your luxury financial resources will be as a percentage of your total income (assuming typical assets at least).
OK, so why doesn’t it keep increasing? Because of the second thing–eventually they cap it at full pay. And then if you keep assuming more and more total income past the point you would be full pay, the percentage of full pay versus total income will be going back down again.
Long story short, I again don’t think of this as a policy position per se, but it is the necessary mathematical consequence of these two policies, only assessing a portion of what they see as luxury money, and then stopping once you hit full pay.
As a final thought, my two cents is the part of this which may be harder to defend is actually stopping at full pay, at least as currently defined. As we discussed, the actual cost per student is likely more than that at these colleges, so why wouldn’t they keep charging at least up to that level?
I think the basic answer is there is a limited supply of students they actually want from these much-more-than-full-pay wealthy families, their presence at these colleges is desirable for reasons that go beyond mere tuition, and so they are competing on price to get them. Given this interpretation, the cynical take would be that once you get to the merely upper-middle-class (85th to 98th types), there are simply too many well-qualified kids from those families to have the same sort of pricing leverage as the wealthiest families, whose well-qualified kids are relatively scarce.
But in any event, whatever the reason for it, the fact they cap full pay at the relevant level contributes to these very wealthy families typically paying a lower and lower percentage of their total income (although once again, assets can blur that picture a bit).