Fundamentally I don't see why people need to establish world-spanning super-conspiracy powers to the wizarding world so it can erase any evidence of magic. Like, the Ministry of Magic is a tiny insular thing that exists to manage the (small, isolated) wizarding population. It has no need to be the Technocracy and turning it into the Technocracy drastically changes its actual role and the amount of agency it gets in human affairs. Giving wizards the level of power needed to do mass neuralyzing of people and actively enforce secrecy of a rather overt set of shenanigans, rather than making them insular and isolated because they're not that powerful, just very well hidden, would drastically recontextualize the Ministry and, well, the themes of the setting. I don't think that if you're building a sensible Harry Potter you want to unintentionally invite R2P comparisons and create a level of callousness about the wizarding world when you don't have to.
And moreover, if you're worldbuilding you're still worldbuilding to a purpose. What is the purpose of the wizarding world? To enable teenage adventures, but with magic. You don't need a force of men in black wearing wizard robes that tell you that everything you saw was just swamp gas to enable teenage adventures.
In fact, the wizarding world doesn't need to be particularly powerful. All it needs is to be whimsical and blatantly supernatural. Yes, that means it probably shouldn't be super low-fantasy, but it also means that you don't need the idea that a single dementor herder is an unstoppable force to anyone who isn't a wizard, and trying to emphasize that aspect just leads to the question of "okay, so why don't the wizards rule as obvious god-kings?"
"Well, wizards don't need anything from mugg-"
"So what about food? Labor? Sex? Worship? Fame? Wizards clearly care about all of these things, and muggles can provide those."
"Er-"