I have been on OOT Yeshiva Day and High School boards (as well as a Mesifta or two) for more than 40 years, following in the footsteps of my father Z”L.
The only time period when these institutions were self sufficient was in the late 1960s and 1970s. The public schools integrated and Jews were in a panic to place their children into all white educational environments.
Large endowments and building contributions bought places for children with no previous religious education.
By 1980 most of those who had lived in the cities had been able to sell their homes and buy.build in the white suburbs and they no longer needed this schooling. The endowments were in place and some continued to donate to annual fundraising drives.
The most important thing these non-frum Jews did was to get Federations to make Day Schools Constituent Agencies. Thus the entire Jewish community helped support Frum Day Schools and High Schools (as well as Conservative, Reform and nondenominational schools.
There is not enough donor money to carry the weight in the frum community. Really good fundraisers understand that the entire Jewish community, businesses and institutions should be mined for resources.