The sticker price of Harvard is not what the median applicant pays. Some applicants -- e.g. Jared Kushner -- literally do pay millions [0]. Others pay a small fraction of that [1].
My 2c: lowering the sticker price at elite schools would be great because it would lower the perceived barrier to entry. Those perceptions matter, especially to folks who don't come from the Professional Managerial class and don't have a clear understanding of how the system works.
But I also see why they don't -- they do, after all, want to make sure that rich families pony up.
[0] https://www.propublica.org/article/the-story-behind-jared-ku...
[1] https://college.harvard.edu/admissions/why-harvard/affordabi...