No, the goverment should not take over the BCCI, because the government would only make it inefficient. The BCCI does a good job on its own, and does not need government help. The government should not be in the business of running something so silly as a cricket organization. That is not a government function.
Despite scandals and controversial bans, Indian cricket should remain privatized and not under control of the government. Sports and their federations should be funded by owners, players and fans instead of taxpayers. India has enough problems with poverty, hunger and homelessness. Cricket shouldn't even be on the Indian government's radar until other problems are fixed.