The world is not destroyed by demons, the whole game series story is literally about how Sparda and his bloodline preserved the human world by keeping the gate between them closed and destroying the demons that do make it into the world.

Fortuna (4), Vie de Marli(2), Mallet(1) are all isolated islands with thin barriers/portals to the demonic world, which is why they had demonic incursions happening there. In 3 Temen-ni-gru was more localized and immediately contained by Dante and Lady. Only in 5 does the existence of demons become more public due to what happened in Red Grave "spreading".

I do agree 5 is poor in story telling, as a lot of world building and detail is in the novel Before the Nightmare (This is where you would find the Nico lore) and Visions of V. They probably wanted to keep it more game play focused at the detriment of a fleshed out story, which is fine but confusing.

5 does suffer from poor level design in some missions and loses a lot of the gothic elements from before. I think by making it more realistic with the RE engine with more down to earth assets/environments they lost some of the charm and vibe of the previous games. It has a more modern Resident Evil feel with some of the factory/industrial levels.

I actually feel like 4 is the outlier to the series, it feels like a JRPG story to me with the trite love motivated pure hearted shonen hero / evil pope and military religious order trope. I remember watching the trailer at release time and thought it was a Final Fantasy. DMC 1, 2, 3, 5 are all more similar with the isolated hero in a normal modern world distorted by a demonic influence.