Games have what I like to think of as a trajectory, generally the answer to the design question, what do I want the game to do. They tend to include solid rules for things right "in the path of the game", less solid rules for actions peripheral to the trajectory, and no rules for things off the trajectory. Some games have broad trajectories, while other have very tightly focused ones. No game is designed to cover all situations all the time, an idea both silly and impractical by turns.
Taking the above into account, it's still not rocket surgery to use the rules given in pretty much any game and adapt them to an edge case. Anyone who is playing a game that's already on the edge of a particular trajectory probably shouldn't complain that their hammer isn't any good at spreading plaster.
There's some merit to this, but I think it's a bit too blunt. D&D, for instance, has almost the same rule for on trajectory as off: GM decides. I think it might be worthwhile to break it down a bit more and look at both what authorities exist, but also what constraints and principles are provided. 5e is, broadly, GM decides as the core mechanic for everything, but there are some areas that provide tighter constraints and guidance than others. Clearly, combat is one. How the out of combat skill system works, though, it a bit hodge-podge, with some areas being well defined and others wide open. I don't think it's fair to say that social interaction is off-trajectory merely because the rules don't provide strong constraints or guidance for social interaction. It's one of the three pillars, after all!
I think it's worthwhile, though, to look at what a game prioritizes, the trajectory as you call it. Clearly, 5e prioritizes different things than, say, FATE. Those priorities are built with authorities (who has say), constraints that limit authorities, and principles -- or guidance on best use of authority. 5e has primarily laid all authority on the GM by using a GM decides core mechanic. This is somewhat constrained by the combat subsystem, in that the GM decides authority is tightly curtailed in the combat subsystem, but still the core mechanic. It also has few principles of play that aren't community developed (which is interesting, to say the least).
To bring this to the topic at hand, 5e does not prioritize professions, or rather, as has been mentioned, it's assumed profession is adventurer. Backgrounds are what you did before you became an adventurer. There's very little support for, either in priority or toolsets, simulating normal people doing normal things. You can do it, because GM decides, but it would be better to embrace the game for what it is rather than continue to play a previous edition with 5e rules. That way never leads to happiness.