Around 20% don’t pay tuition I believe. But keep in mind that Harvard tilts heavy toward grad student population, and selects heavily for students that win fellowships and this brings in outside money (that is how I got to attend) and master’s students who typically pay full tuition. Among my PhD cohort, it was a common joke to say that 1 graduate student was funding X free undergrads in the department (given that we were all supported fully, including insurance, by outside funding).

20% of undergrads going tuition-free is just part of Harvard’s marketing budget. It’s not philanthropy, just the cost of doing business if your business is elite status signaling.