A Yeshiva Built With Public Funds - Does The Family Get To Choose Who Leads The Yeshiva? Rav Shraga Feivel Mendlowitz ztvk"l said a resounding no!
This is not a new thought - The same question was asked of the yeshiva in Volozhin.
CHANGE OF LEADERSHIP: A FAMILY AFFAIR
After Rabbi Hayyim’s death in 1821, the leadership of the institution
was taken over by his son, Rabbi Yitzhak Berlin (1780-1849). For the
next decades, the yeshiva remained a family business. Rabbi Yitzhak’s
death caused his son-in-law, R. Eliezer Yitzhak (1809-1853) to become
rosh yeshiva and when he died, the mantle of leadership passed to his
younger son in-law, Naftali Zevi Yehuda Berlin, the Netziv who governed
it for four decades.
Secular Studies & Volozhin - The Entire Story!
https://blogs.timesofisrael.com/volozhin-the-rise-and-demise-of-the-mother-of-all-yeshivas/