Please don’t throw this number out without understanding how it really works.
55% of Harvard undergrads get some sort of financial aid. Much of this aid is in the form of grants that cover tuition. One simple example — if a student’s family makes $65k or less a year, tuition is free. Above $65k, there is a sliding scale, and financial aid officers have quite a bit of latitude to work with people with unusual financial situations.
To be fair, I think families making $250k-$350k in high cost of living areas might get the short end of the stick in this system, but even they have some flexibility if they work with the financial aid department.
Love or hate the top Ivies, they open up doors (or at least fast-track you to the door) that remain closed for a lot of graduates.
If your only goal in life is to maximize your chances at some cookie-cutter prestigious professional job / career, then $200k isn't too bad. The ROI is going to blow most everything else out of the water, as far as education goes.