I think that people may be confused as to what’s happening with this announcement.
The early phase details of the agreement were negotiated first between Harry and Lucius. Harry represented house Potter here because he’s the entirety of house Potter. Lucius negotiated with Harry because Harry (as the boy who lived) has a lot of clout and credibility and he offered to throw that behind Draco. On an emotional level, HP also offers revenge against whoever attacked Draco and the possibility of revenge against Dumbledore.
Step two, the adults negotiate amongst themselves. In this second phase Lucius goes to the board of Governors with the agreement he and Harry made as a starting point.
The Knott and Greengrass votes are naturally inclined to go with Malfoy by faction alliance. Knott is also incentivized to go with the plan for other reasons. His son is a friend and chief lieutenant of Harry Potter. That’s a potentially very valuable connection, but its a connection that can’t be used when the votes are split death eater v Dumbledore. Realignment effectively “monetized” that asset. Greengrass doesn’t have that and so asks for a few sweeteners on its deal. Also, the plan reduces their children’s risk of death which is a non trivial inducement.
Bones runs the aurors. That’s a strong base, but the aurors are generally kept out of Hogwarts, which was previously described as an invincible fortress. This puts her people inside Hogwarts which expands her domain of influence. While she probably wouldn’t be willing to do that at the expense of being kicked from the order faction to the death eater faction, its worth it if she gets to keep most of the same allies (which she does via Harry) while isolating Juergen and other of her more extreme opponents. Also, the plan reduces the childrens’ risk of death which is a non trivial inducement.
Neville inherits the Longbottom vote when he turns 18, so Longbottom is in Harry’s camp in the long run and so his aunt has reason to at least reap the benefits of being on Harry’s side since they pay the costs regardless. Like Bones she benefits from isolating extremists like Juergen. Based on her comments in prior chapters both at the war game and about QQs speech she favors a higher level of military readiness and is getting that from this deal.
So once the adults agree on the deal. Why announce it this way vs some other way?
An announcement through official channels goes through Dumbledore. Bypassing that contributes to sidelining / undermining Dumbledore, so Malfoy has a clear interest in the announcement through non official channels.
For Bones and Longbottom an announcement from the board has the two of them seen as going along with house Malfoy. Given their current alliances this would be damaging and bad for their images. By having the children give the boards’s announcement right on the heel of an announcement by Harry and Draco the optics are that Draco is bringing the Greengrass / Knott votes and Harry is bringing the Bones / Longbottom votes. This allows them to maintain the optics of their factional alliance. They are seen as Harry’s votes rather than as Malfoys votes.
Greengrass and Knott are in similar situations. As parts of Malfoys faction they also benefit from sidelining Dumbledore. They are lesser houses than Malfoy and are voting with Malfoy and are seen to be voting with Malfoy. Their houses get much more visibility and ‘airtime’ with this plan than if the board announced a vote. The chapter notes that it had all been negotiated and rehearsed and that the prominent role Daphne got was one of the carrots thrown to Greengrass.
Basically it happens this way because it is in the parents interests for it to happen this way.
There has previously been some speculation that the dark lord in Harry’s birth prophesy is death rather than Voldemort. I think this interpretation just got a lot stronger.
James and Lilly had defied Voldemort but not death. The new lines back an interpretation that the Peverells thrice defied death with the three deathly hollows and Harry is born to the Peverell line.
This is, in some ways, a more natural interpretation of that clause since James and Lilly were in the Order and were defying Voldemort on a daily basis not just 3 times. The line of the Peverells makes the number three make sense rather than being arbitrary.