Pohtan is working for a 'prosperous future' and to eliminate exceptional people, the problem is that at no point did she say a 'prosperous future FOR THIS CITY' and she's mad at exceptional humans for killing the demon lord. Yes, she's working for a 'prosperous future' for an undefined group while eliminating or subverting anyone who could challenge her plans.
You're overthinking this. It's already been made clear for many chapters that Pohtan is working for the benefit of Idazig and that she isn't doing it alone. In fact, she can't do it alone. She herself is kinda useless (as her moniker indicates). What Pohtan has done is simply to facilitate the City Council's efforts to achieve the same goals she seeks to achieve by providing leadership, a rational mind, and firearms. The rest of the crazy stuff that's been happening have been the result of actions taken by the pre-Pohtan bureaucracy and their idiosyncrasies. The fucked up timeline is the fault of the Verification Office. The barrels (and by extension children-hunting) are the Mages' Guild taking things to their ultimate conclusion. The postal vs messenger war was inevitable thanks to the haunted PO chief. The religious suppression is the Church going wild. The brainwashing (and existence of "Cats") was the bureaucrats' plan all along. Also, most of the bad stuff happening on the streets on a regular basis are just the citizens being their usual idiotic selves.
The thing is, like many have pointed out here, THE CITY OF IDAZIG ITSELF IS EVIL. Pohtan only gave the already-messed-up Council and bureaucracy a focus and made them able to competently act out the things they'd wanted to do for their (often personal) benefits. So yeah, Pohtan's work and her prosperous future are benefiting the City. The EVIL City. There's no question about that.
Oh, if you've ever read Discworld, Idazig is basically set up almost exactly like Ankh-Morpork. It's just that the latter has a more properly evil and competent Patrician.