This is a huge myth for HYPS (and M as well). You are underestimating the financial aid that HYPMS gives out each year.
I would go as far as to say that for the majority of people in the country (i.e., those making around 125k or less), HYPMS are probably the MOST affordable schools in the country* (yes, usually cheaper than state schools). *(only exception being full-ride merit scholarships but even still, HYPMS need-based aid often comes close)
If you make 100-125k (with normal assets) you basically pay only room and board (in other words, tuition is essentially free). If you make around 65k or less, you essentially go there for free (except some small work-study amount).
Now if your family makes 200k, then yes, HYPS is kind of expensive. But your family also makes a lot more money than the majority of people in the country so theoretically you should be able to afford a greater portion. However, I do see how families who are in the 180k-300k range might feel most "screwed" since they don't really get need-based FA but 65k/year is still a lot.
And if you are going to HYPMS with a sibling, expect even better FA than what I just listed above.
The tier of schools just below HYPMS (e.g., Penn, Columbia, Dartmouth) have financial aid that is similar to the level of HYPMS (but expect to pay maybe 5-10k more per year). Even still, they are still quite affordable if you really are in financial need.