and should be at any table
See, this statement right here that you nearly start with is what is... offensive. I'm an old and entitled grognard; and even I don't believe that anyone outside of a table gets to tell those at a table what they should be doing.
Wouldn't such families do what we did in reality and try to keep the power for themselves?
Depends on the setting. In some settings, sure. But in all settings? Uh, no. You don't get to tell others what they should be doing.
Now, you could make arguments about how useful, interesting, beneficial, etc about how doing so in a setting can be. But in every setting at every table? No.
Artificers, similarly, have this problem. They exist in most D&D settings for the purpose of existing.
My experience is that artificers actually don't exist on most settings. Outside of Eberron, I don't recall any of the settings in which they are canon. Of course, I would never suggest another table should allow them in the Realms or GreyHawk or Dark Sun. But my experience is that no, they don't exist in most settings.
But what are some character classes that you feel need some kind of narrative anchor to not feel "Extra"?
Warlocks. Agree with you on this. Without a setting tie in and cultural impacts, to me, they are just an excuse for a different set of mechanics for magic. But, even though, I rarely implement such in my settings that I allow warlocks, because I'm lazy.
Characters are built on character, not stats. Being royalty, a merchant's child, a former criminal, etc... all should have more of an effect on who they are than their class.
I agree with this. I cringe when I play at tables where "classes" are tied to some sort of cultural label. Fighters don't claim to be "fighters". Nor rogues, or in most cases other classes. Sure, in most settings their are people called "wizards", "clerics", "sorcerers" and such. But they might go by other names too, and what they are called in common doesn't mean its a class.
But, again, it's not up to me to tell others what they should do at their tables or how they should envision their settings.
Warlocks are a great example of this phenomenon.
Yep, as said above, this is the one that I have trouble with. But to me this is because the power comes from a specific entity in the lore and not something that is nebulous to the settings (the weave, dragon blood, etc)
But beyond mechanics, things should have a narrative connection to the setting. Something that a player can look at and say "Yes. That is the setting's narrative for my class and I like it and want to explore it!" or "Yes. That is the setting's narrative for my class and I would prefer to not have that."
Yea... no. You settings or your table, great. Go for it. It can help build a rich and interesting settings and add depth to a campaign. But it's not the only way, nor does it mean one game/table/campaign is objectively "better".