I can see some problems.

Zero: What do you mean by technology? What do they stop using? Computers? The gear? The wheel? Explosives? Electricty? Clothing? Fire? The term "technology" covers basically everything mankind has developed. If a modern human were to try to survive with absolutely ZERO technology, they would quickly die. Humans are kind of shit without some level of technology.

One: What caused this apocalypse? What kind of apocalypse makes people go "You know all that stuff humanity built before civilization blew up? The stuff people figured out and we clearly had some idea of how it worked during our lifetimes? Well, we'll NEVER be able to do that again"? Wouldn't having more tools and weapons help survivors survive better? Wouldn't they WANT to keep some amount of technology? If technology caused the apocalypse then it would make more sense that some people might stay away from it.

Two: "notion that those arts could be easily recreated simply by studying old books" I'm not sure that's exactly true. Sure, you can learn about said "arts" from books, but to actually do it is another thing. It's one thing to read about photo-etching transistors for integrated circuits and another to get the equipment, generate the power, get a clean enough space to set up all the equipment, get the silicon and dopant, create the masks and design and etch the traces.

Three: I think the mentality of "I have less pride now that I figured out how to generate light using a potato because it shows my god-ancestors weren't actually gods" is not realistic.

Four: common sense and science. Let's look at an example: It is common sense that things can only be in one place at a time, right? Well, our studies in quantum mechanics says otherwise (see double slit experiment); things on the quantum level (like electrons) do not follow the rules that we think should apply according to our common sense. Science requires QUESTIONING everything. If scientists were to dismiss anything that was counterintuitive as "It's common sense, it never works like this", scientific knowledge would go nowhere! We'd be stuck with incorrect assumptions on how the universe works.

Five: If said nations are so scared of technology that they are going to ditch everything it would probably take more than one lost fight to change their minds.

Worshiping technology is plausible, I suppose. Might be interesting if each small nation just forgot how to build new things and just know/are only able to fix what they have. The original survivors could have settled in a power plant and some dedicated most of their lives keeping the power on. Another set of survivors, a railyard. Each set of people just know the basics of how to keep a few select things running. Instead of people purposefully forgetting how to build new technology, more and more pieces of information are lost with every generation to the point at which the mechanics are basically monks keeping relics and shrines to old humanity running. The rest of humanity is just trying to grow enough food to survive.

Once food isn't a big problem, though, things get interesting. Travellers talk of other settlements which each have their own wondrous treasures; a town which is lit at all times; a moving settlement powered by wood and water. Eventually, these stories reach the ears of someone in a position in power. Someone who wants all of these things for themselves.

I feel like this has probably been done before, though, but don't let that discourage you.