Rolemaster has had this since at least 1984.
Oh, the "No Profession" Profession? I mean, kind of, but it's really more about building a jack of all trades, as I recall.
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I don't know about Fighter as an "everyman"
per se, but if you have a character concept like "farmboy", "trail guide", "assistant pig farmer", "random modern day person thrust into a fantasy world" who suddenly goes on an adventure, the current class model isn't going to work out very well. In earlier forms of D&D, you could squint a little bit and use the 1st-level Fighter as a chassis for such a character, but that didn't mean it was a perfect fit either.
I remember reading Ed Greenwood's
Spellfire- Shandril was a barmaid who went on one short, ill-fated adventure before discovering her anti-magic superpowers, yet officially, she was a 1st-level Thief, somehow able to backstab and use (probably badly) several Thieving abilities, which didn't make a whole heap of sense.
The problem here is, D&D was never intended to accurately model a Bilbo Baggins, Holger Carlson, Taran, Garion, or similar characters. The fact that even the "simple" class carries more baggage these days that you can't really explain away than it did in times past doesn't help, but it wasn't like I could say "ok, so my character concept is a 14 year old girl from Coal City, Illinois" and say that justified the higher hit die and ability to use advanced weapons and armor she would gain as a 1st-level Fighter- it was just a little easier to swallow than her being able to cast spells or pick locks.
Of course, it's worth noting that even before the modern Isekai boom, the "Earth character who ends up in a fantasy setting with special powers/knowledge" trope was well established- John Carter gains superhuman strength on Mars, Dorothy Gale gets awarded a powerful artifact within minutes of landing on Oz, Corwin of Amber is actually a superhuman demigod with centuries of combat experience- he just has amnesia. So you could justify such characters, if you're willing to accept the "everyman hero" receives a little boost- in
Three Hearts and Three Lions, as I recall, Holger Carlson finds he has the ability to speak the local language, ride a horse, and use weapons and armor right off the bat (though, again, as I recall, we later find out he's the reincarnation of a great hero- reincarnation being another way to justify this sort of thing, as seen in The Wheel of Time series).
I'm not saying it wouldn't be nice to have a way to model characters without assuming they have been given divine protection or special powers to keep up, but that ship sailed long ago- the only way you could really do it is if the entire party has a similar background. Otherwise, you're going to be on the back foot in a party with regular character class levels- and yes, I count the idea of "preternatural luck" to be a "special power".
Someone upthread mentioned the Warlock, and that might be the best class for this sort of thing- lots of stories have characters who have a brush with the supernatural at the beginning of their stories, which allows them the ability to stand on their own two feet. I understand that's not exactly ideal if you don't want to play a Warlock, or you want a strictly non-magical character, but it is what it is. Unless of course, you're perfectly fine with not having characters with somewhat equal ability to perform in a dangerous adventure, at which point you could just not use all of your abilities until such time as you feel they are justified- but make sure to discuss this with your group beforehand!