Either Dumbledore is grossly incompetent and it makes you wonder why he's still Headmaster (let alone all his government positions) if he's this bad at it, or he's deliberately sabotaging his school for some reason and has been since he became headmaster. I'm torn on which to think is true. Either way, why is he still headmaster?!
Honestly the idea that the curse doesn't exist makes sense considering how out there it is compared to the rest of the magic we see. But something has to be sabotaging the defence position but why does it have to be Dumbledore?
Considering Voldemort's personality he totally would decided to get revenge on anyone he perceives as 'usurping' the position he deserves. So making it as goal to tear down the reputations or serious hurt/kill the DA teacher is totally something he'd do. And his followers would agrees assuming he was trying to weaken any threats to him not that he's doing it out of spite.
Then once the first few teachers suffered horrible 'accidents' rumours of the 'curse' start spreading possibly aided by Death Eaters. That will make many people reluctant to apply for the position reducing the candidate pool. The ones who still do it will tend to be arrogant making them easy prey furthering the reputation of it being cursed.
So by the time the war ends few are willing to take the position and Dumbledore is desperate for teachers. This would compound his already questionable skill at hiring leading to the teachers we see in canon.
At least this would be how I would do it without making Dumbledore as evil / an idiot. Since even if he's a pacifist I don't think he's idiot enough to sabotage it while there's a war on. restrict it to non lethal spells and how to escape yes but outright sabotage it completely no.
As for lack of research, her having the Statute being put in place because of the witch hunts, at a time when they were basically over and the Salem Witch Trials being one of the specific incidents cited. Also, witch burnings were mentioned in the story at one point, despite that never actually being a thing.
My personal headcanon is the secrecy was merely formalising something that already existed. Apparently it didn't receive that much protest and the transition happened fairly fast with minimal issue. So suggesting that most wizarding homes were already hidden and had slowly become self sufficient over the last few centuries to avoid the witch hunts makes sense.
So it wasn't ordering everyone to hide away. They already were it merely made it illegal for those minority who wanted to use magic openly to do so.
Or at least that how I would reconcile it with our history. Obviously you can change history but well pop culture history is funny but wrong since people are people.
Honestly, I generally consider the whole Wendelyn the Weird thing pure propaganda. And no magicals dying from the witch hunts? (witches were hung in England as an aside) It's a bloody guarantee muggleborn children died of it. I personally like to imagine Slytherin having advocated to either not inform the parents of muggleborn or to take the children and have magicals adopt them. Which during the actual witch hunts would have been a pretty damn good idea at that.
That people think he was against muggleborn ... well, it has been a thousand years, so propaganda, things taken out of context ...
To be fair with the magic we see a trained witch probably could survive easy. If there not caught off guard or make a mistake. And of course trained is a key word. A witch going invisible; apparating; or protecting themselves all requires warning and knowing the right spells. So an adult could probably do it if there not unluck but a child? Accidental magic might change it but realistically your going to have a decent number of death kids and not all of them muggleborn. Oh and accidental magic would also be harder to hide away making it easier for them to find magical children.
After all if your house isn't hidden by charms what's stopping the muggles attacking a wizarding household? or waiting until you leave the house and then grabbing you. An adult might escape but a child could unwisely leave safety to play and get killed.
Oh and this leads me to an interesting thought about the consequences of the witch burnings. Even if magic allows you to easily survive a witch hunt, what about your belonging and house? Unless your a traveller you live nearby and there probably going to steal/burn your belongings/house as well as you. And your certainly not just going to be able to go home and act as if nothing happened since next time you go out they'll try again.
So even if you not physically in danger your going to lose a lot to the witch hunts. Muggle repelling charms would solve that but then you can't talk to your neighbours so have to go further for supplies. Muggles villagers would be suspicious and if your travelling anyway magical enclaves are just as practical.
At that point your just undergoing an early form of the secrecy and forming your own community sperate from the muggles. Which is my headcanon for how it formed with each enclave deciding to do it themselves and once a critical mass was reached the international version was forced on the rest.
So yes it undoubtably the history lessons have a lot of propaganda to white wash the threat. That also occurring with Slytherin makes a lot of sense.
Unless your name is Sirius Black, apparently.
To be fair Sirius was already on his second chance. Namely the Snape incident. Sirius almost got Snape killed or infected and either way Remus probably would have been executed by the ministry. Basically a betrayal of Remus. Not to mention the extensive bullying of the Slytherins.
Dumbledore could have easily decided that was his first chance and regret not expelling him. After all in hindsight it was clear signs he didn't value his friends and was willing to murder people using others as tools.
Obviously not true but easy to conclude from Dumbledore perspective. Of course how Sirius acted with HP and Hagrid should have confused him enough to investigate but the assumption of guilt make sense.