I'd forgotten earlier, but there is an anime that almost justifies an "everyman" concept as a D&D character class, thinking about it. "Handyman Saitou in Another World" has a main character who was a talented, but pretty much regular handyman who is able to ply his knowledge of all things mechanical into a support role for a party of adventurers, which includes dealing with traps and locks (as he worked as a locksmith, among other odd jobs), which almost makes him a viable Rogue/Thief- Sneak Attack, not so much though.
While he has no special powers, it occurs to me "real-world education" would be valuable in a game that really valued skills, and especially, something current D&D has, but doesn't use very well- Tool proficiency.
Tool proficiency covers all sorts of things most adventurers only dabble in, from disabling traps, driving a wagon, playing musical instruments, or playing games of skill or chance. So maybe a hypothetical "Everyman" class could have more Tool proficiencies, and more/better ways to use those tools while adventuring? Tales of the Valiant has a martial "Mechanist" class (though they quickly evolve into dealing with magic items and temporary enchants, with the subclasses going straight into purely magical effects), which might be a good start.
Ultimately, though, I think the issue is that D&D has only occasionally been a skill-based game, with only 2e having a vast list of Non-Weapon Proficiencies one could employ to decent effect- until the pendulum swings back into making downtime activities (negotiating with NPC's, bartering with merchants, doing research, crafting, gear maintenance, scrounging, and so on) and serious exploration challenges, there's not much room for a purely skill-based character.
Though I have heard people who manage to run 5e in this style, despite the abysmal skill and equipment options, so maybe it's not all gloom and doom.