Well, that's just RAW per Gygax's explanation of why training gave no XP in the DMG, and why levelling up through adventuring was largely unrealistic and yet supported by the rules. My point though is that he deliberately gave no mechanics for players doing any of that.
As for "a level every few years of constant work" it would have to be much slower than that, otherwise you end up in a Forgotten Realms situation where every merchant and barkeep is over 10th level and you have incoherence about what meaning 1st level characters would have in such a world (to say nothing of normal orcs) - season up a few years and come back at 7th level sort of thing.
Everybody kind of has a limit as to how good they can get at any given profession - the old (and quite true) saying that people rise to their level of imcompetence holds sway here.
But sure, someone who has been a merchant for many years and has an aptitude for it might well be an expert. And an Orc that's spent many summers raiding and fighting (which, after all, is just adventuring in a different way anyway) could very easily have become equivalent to a mid-level Fighter in terms of martial prowess.
Imagining that there is something that a character can do to earn 1 XP a day (and if you've read my 3e posts on NPC classes you'll see where this is going, but it works even better for 1e because of the exponential leveling), then a fighter levels up after 2000 days of training - about 7 years or so. He then levels up again after another 7 years, then again after another 14. He's now perhaps 45 to 50 years of age (persumably he's now also the veteran of several real combats as well) and a Captain and civic leader.
Sure, that's what I'm getting at; only some of 'em will earn on average more than 1 xp per day and some will earn less. Same goes for street Thieves, temple Clerics, lab Mages, travelling minstrels, and so forth. And there too, competence limits can apply - the 2nd-level village Cleric might have gone as far as he can in such things given his situation and surroundings, but is content there, happy with his life, and could be a 2nd-level Cleric until he dies of old age.
He levels up again, but is now in his 70's and aged and his body failing him and he's not able to employ his vast experience as his Strength has fallen to a mere average level and his Dexterity and Constitution are mere 6's. His hit points are lower now than they were when he was lower leveled and youthful. This is very much my demographics in 1e or 3e (A)D&D.
If this guy retires from soldiering at age 50 and doesn't keep his hand in by training others* or just staying fit, I have it that his Fighter skills will decay over time; and wrote up a system for this (filling what I see as another huge hole in the rules: what happens to someone's class skills after retirement).
Worth noting that the other game precept violated by these stay-at-homes is formal training rules. That village Cleric probably trained himself, very slowly, over the years (assuming no unusual divine intervention). Ditto a lab Mage: instead of formal fast-track adventurer-style training that takes a week or two, she probably trains herself into a new level over a year or two.
* in Game of Thrones, every single member of the Night's Watch that lasts more than a few months is or becomes (the equivalent of) a levelled Fighter or Ranger; and most of them slowly advance in levels the longer they remain there and don't die.