As for why the Board of Governors, despite suffering such unfair treatment, had not chosen to withdraw its funding...
One had to know that the vast majority of Hogwarts School of Witchcraft and Wizardry's Board of Governors members came from Pureblood Families, and among the descendants of those Pureblood Families, quite a few had joined the Death Eaters.
The upright ones were easy enough to deal with. They had supported Dumbledore's decision from the start, so naturally they would not resort to withdrawing funding to threaten him.
As for those with guilty consciences, they dared not do so even more. After all, as members of the Board of Governors of Hogwarts School of Witchcraft and Wizardry and public figures in the British wizarding world, their addresses were semi-public.
No one dared guarantee that Linley and Irina, those two newly risen Demon King level wizards who were not bound by the rules, would not decide that having heard the truth in the morning, they could die that evening, then show up at their homes to "check their water meters."
If those two Demon King level wizards barged into their homes and discovered that one of their descendants was a Death Eater, setting aside the ruin of their reputations, the Ministry of Magic's current attitude toward Death Eaters alone was enough to make them deeply wary.
The execution of that descendant who had joined the Death Eaters would be a minor matter. If it implicated their family and caused it to decline, that would be a price they could not bear.
To maintain the current peace, these Board of Governors members with guilty consciences had no choice but to publicly support Dumbledore's decision, "willingly" becoming Hogwarts School of Witchcraft and Wizardry's ATMs.
Meanwhile, Frey Castle, fourth floor.
Within the training ground