UTJ and Shas will only join the government if the government agrees to cancel the plan to conscript the yeshiva students, forcing them to either go the prison for at least several years or to the army for several years. They won’t have the ability to get high levels of funding restored. Remember there are plenty of anti-religious parties ready to take the place of the hareidi parties, so they really don’t have much bargaining power. The attraction of the hareidi parties to Netanyahu is that they are concerned with what to him is a tangental issue (conscription), and will leave the important stuff (economics and national security) to others.
While the yeshiovos allied with the Eidis Hareidis never relied on government funding, the other non-zionist yeshivos have seen why relying on secular Jews for money is a bad thing.