The cessation of setting your story in real-time or having them age at all can have it purposes, but for some varieties of stories that are character driven and thus depend on the development of both its cast and the narrative in context of its period, this can be ruinous.
Sliding time scales sees the main character and/or their cast frozen in a specific time period, where they will not grow older and overall death does occurs rarely if at all. The genres that feature this range from comedy to action. Whatever the purpose, it can remove the tension from a narrative.
Anthony Stark was conceived as a arms-profiteer during the Vietnam War, only in the post bellum period was the character rewritten and redefined as he has become today, most notably as portrayed by Robert Downey, Jr. Nevertheless, he along with characters such as Francis Castle, “the Punisher”, are inexorably connected to the war and cannot as easily be temporally removed into some amorphous modern era. Similarly Benjamin Grimm and Reed Richards of the Fantastic Four took part in WW2 – Grimm in particular excelled as a fighter-pilot hence his fame and eventually position as pilot of the space-craft that led them to getting their cosmic powers.
As such, Grimm & Reed are both from the 1910s, Stark and Castle are from the 1930s, and as such all of these would be either dead or extremely senescent.
Nick Fury in particular was a prominent comic-book hero, whose career stretches from WW2 to the Vietnam War and has along with Steve “Captain America” Rogers had the unique exception of keeping their original eras of birth.
Rendering them as permanent inhabitants of a world of a sliding time-scale deprives the characters of their backstory and narrative purpose. Immortal and stagnant rather than lively and exciting.