It's ill thought out because it misses karmic demons and ogres? Ogres can apparently destroy whole cities so they aren't minor threats. They made their whole societies around preventing ogres. It's definitely something they need to consider. It also appalls me that they don't even have contingency planes like anti ogre weapons readily available let alone ogre hunters. I think the original leader was very incompetent and the remaining brainwashed townfolk unsurprisingly didn't bring much else to the table either.

The society became primarily concerned with ogres and karma demons when they gave themselves the death of shame. Before that, the concern was PK users going around raping, enslaving, torturing, and murdering folks. Which they are still doing now, only to the monster rats.

It is incredibly easy to control soldiers even if you give them powerful weapons. Wars would be impossible if this were not the case. Like I said before you can have multiple ogre hunters that don't know of each others existences and/or are kept skeptical of each other. They can also be replaced frequently. They too can be brainwashed. You can make robots. You can use less dumb anti ogre weapons.

... Armies have taken over their own countries many times throughout history.

The biggest reason PK users managed to slaughter the other 99 percent of humanity is because they have PK, and the rest did not. The reason the PK emperors managed to dominate their non-PK slaves is because they had PK, and the slaves did not.

If you give some the ability to kill by the power of their thoughts, and not others, then you get more slave empires. At least by how this series considers human nature: perhaps you disagree with how cynically Shin Sekai Yori views humanity. As far as this anime/novel is concerned, if you give people power, they abuse it.

If you brainwash them, you make them stupid. This is why Group 1 was not brainwashed. And this society can't make concrete, let alone anti-ogre robots. And you are underestimating the power of PK: the armies of the 21st century were not able to defeat the PK users, despite PK users making up less than 1% of the population. A robot would be ripped to little metal pieces.

29 previous ogres were stopped one way or another with humanity still existing. They seem to affect ~1 city before being eventually brought down.

We do not know this, as ogres appeared before the dark ages. Perhaps most of them appeared in the 21st century, and mostly killed non-PK users.