Societal reflections of post-apocalypse and decadence

[Johnny.JJ]

... all knowledge from the Scientific Revolution and beyond getting muddled into something as error-prone as Medieval alchemy.

Sure - something along the lines of this.
Some of the most conservative magic technologies (the basic stuff) would still be working in the post-apocalyptic word, but rarely anyone would have the capacity to maintain these machines (yet alone repair them in case of breakdown). Fixing such a machinery would involve parties of scavengers searching the old ruins for identical spare parts. No more engineers, more like charlatans.

This is also about social stratification: the most primitive societies consisted of hunters and gatherers (later on replaced by farmers); scientists, artists and all this sophisticated bunch - i.e. people who do not produce any directly usable values - would be unlikely in such an environment.
Take wheat for example: there is a radical difference between having 1:3 and 1:50 yield ratio (complemented by superior agricultural machinery). Less food equals less resources to support the people who produce no primary values.
Therefore, I'd be expecting that starting 25% literacy rate to be on the decrease, in most areas.

How society responds depends on how much pre-apocalyptic knowledge is retained. Assume the global population went from 1 billion to 50 million in a short time, there's a 25% literacy rate among survivors, and growth rate of x2 for first century, and x1.3 for the next. You'll go from 50 million to 130 million in 200 years

That is pretty close. I was thinking of 2 billion going to approx. 100 million after those ugly 200 years.
It seems that our math is governed by similar principles.

Society is going to be local, assuming no world-shaking magic or monsters. Each cultural region will have developed their own set of belief systems, each quite disconnected from their neighbors, which could lead to conflict when two cultures link up.

Culture clash is a solid concept that should be used to its full potential, at least in such a savage world (the new cultures would have little experience of coexisting in tolerance - the first conflicts should thus be the bloodiest ones, I think).

you might get an empire or flourishing culture in the most ideal of geographical regions ...

... to diversify a region from all the savages - why not! However, for some reason, I was thinking of "unhealthy" empires as well* - paranoid, dogmatic, corrupt to the bone by naked power grabs, etc.

*)since the earliest attempts of government are usually the most unstable ones

Some societies may borrow from the fallen civilizations, but history shows that Western culture drastically shifted away from Roman culture after the latter collapsed. After all, it took more than 200 years after the end of western Rome for republics to once again be commonplace in Europe.

I'm not sure this is the same. The Roman republic wasn't a republic in the sense of a modern state - it was rather isolationist, unable to provide a more decentralized model of ruling (one of the reasons why it collapsed). In other words, Rome was not fit for the upcoming societal changes in the world, and it refused to adapt. The cultures that came after Rome did not preserve the social model of Rome, for Rome was a dead end. Also, the "barbarians" were not direct descendants of Rome.

In case of this little fantasy world we're debating, the people in the post-apocalypse are basically just sitting on the legacy of their ancestors - they may decide to keep some of the ways of their ancestors - as long as these old customs are still usable in the changed world.
Also, instead of throwing away the unfit customs, they may just re-tailor these to fit better into the current situation.
All this relates to how highly is traditionalism regarded in a region, though.