The economic rationale behind the Asian cap is donor money. It is likely that Harvard receives most of its donations from wealthy White individuals. If the school became seen as "too Asian" these donors would stop giving. Why give money to an institution they see as not benefiting "their" kind?
If there was no cap at the Ivy League schools, America's elite could become predominantly Asian American within a few generations. This sudden demographic change would receive major backlash and resentment from the White majority. The United States, whether you like it or not, is still a White, Western country that primarily serves this group's interests. No group relishes in seeing themselves become a minority in their own country.
Suppose the top universities in China became overwhelmingly White. Do you not think there would be backlash and attempts to limit their numbers as well? Of course there would.