Okay, so, picture this.
Following Voldemort’s (first) defeat, Dumbledore is the most powerful and popular political figure in wizarding Britain. And so he and Bagnold (who knows she’s on the way out now that the war’s been won) use the temporary backlash against blood prejudice to work in progressive legislation and judicial rulings. As head of the ICW, Dumbledore works towards international change as well. For a while, it works. Even when Fudge replaces Bagnold, the legal framework and ministry culture continue to change for the better - slow but sure.
Then comes the backlash. Lucius Malfoy and his ilk see the writing on the wall and realize they are getting worked into a corner. But, they can’t out right rail against the perceived outrage; people are still wary of dark lords and out right prejudiced idealology. So they get to Fudge and figure out his weaknesses are power and greed. Fudge’s pockets become heavier and, the more Lucius talks, the more worried Fudge becomes of losing the support of the people and his position as minister. And suspicion starts being sown into the minds of the public that maybe Dumbledore has his fingers in too many pies. Oh, no no, he’s still a good wizard, the only wizard He Who Must Not Be Named feared, but why are we still fixated on the war in this time of peace? The ICW, tired of following Britain’s lead, starts to disengage as well.
And so, Dumbledore finds himself still respected and near mythologized but entangled in a dangerous game of not overreaching least he finds himself Public Enemy #1. He’s not worried, though, because there’s always Hogwarts. And while he’s neglected his duties a bit in his quest to affect change, he knows Minerva has handled things admirably. Except. Snape has made things near unbearable under his guise as double (triple?) agent. The rest of the staff has been near paralyzed by Dumbledore’s absentminded assurance that, “No, no, I’m sure Severus means well. Surely you’re over exaggerating, Minerva (Fillius, Pomona, and so on and so on). And now he can only curb the worst of his spy’s behavior because certainly it would be suspect if he was reigned in now.
As more and more children of war veterans (heroes and villains) trickle in, it only gets worse. The governors make it near impossible to change things: an updated Muggle Studies syllabus, a living History of Magic teacher, an investigation into why DADA professors only last a term…it is all shot down with the implication that they’ll use it to further chip away at the Headmaster’s influence. And Snape just gets more vicious and the other professors become more disillusioned and it’s a never ending downward spiral. So, by the time Harry gets to Hogwarts, Dumbledore, while a celebrated public figure, has very little in the way of real power. At this point, he’s pretty much attempting to put out fires as they appear but can never stomp them out completely.
So, while it would still be utterly terrible that he left Harry (his secret weapon, the only one who can defeat the probably not dead Voldemort) with the worst sort of muggles with no follow up, it would at least make sense. He got caught up in trying to change the world for the better, then improving the school he loved…and the fate of one little boy who was supposed to be safe as houses just slipped his mind. At least then, it would be understandable why the most powerful and respected wizard (both at home and abroad) was reduced to secrets and riddles and the political version of battlefield surgery (all you can do is stop the bleeding and hope for the best).
As it stands, we’re left with a lot of excuses and a really poorly named child.