One thing I would add about this though is Conan is very episodic which lends itself well to the rootless wanderer (though in some stories he clearly has roots and responsibilities). But D&D is week to week, and each session builds on the previous one, so while I think it is true most characters in a standard D&D campaign start out as rootless wanderers, over time they tend to establish roots. And lots of people tire of the rootless wanderer trope and try to establish more connections at character creation.
Yet I've almost not seen this. The only thing I've seen do this, in general, is either players who heavily focus on it and have good GM support for it, or the name-level stronghold stuff, which can sort of do it (but often doesn't). In terms of classic and really trad D&D play, not really. All the high level characters I can think of in the campaigns of the three D&D DMs I played with through the '80s and '90s, I never really saw this happen. The two main high level PCs I played, neither one had any family, no defined place of origin, no backstory ever developed, and neither of them even particularly had much of a base of operations. My wizard theoretically had a wizard's tower, but I don't think anything of consequence ever happened there. My ranger had some followers, and I guess they all theoretically wandered the forests when they weren't slaying demons and such. They had allies, other PCs mainly, but not really any normal human relationships. That was the normal and usual D&D character from 1975 to the very end of TSR D&D!
Not to say that what you are relating doesn't happen, etc. Its just really fantastically rare, even in campaigns that feature a lot of creative material and really captured player's interest in terms of the action and whatnot. At best it was just assumed PCs went somewhere and hung out, maybe they had girlfriends or something? Frankly, why create that sort of stuff when playing D&D, its all about XP and loot, personal entanglements are just a bad idea.
Also wanderers don't have to be rootless. Wuxia is filled with characters who wander around fighting protecting the weak and contending with corrupt officials and people who use power to exploit. But they are often characters with very strong roots in a martial organization (i.e. Wudang, Shaolin, Plum Blossom Island, etc), roots under master or group of masters, and powerful family connections (the character in return of Condor heroes is the son of the villain of the first book and is adopted by his father's sworn brother, the first books hero, then placed into the care of a Daoist sect). That can absolutely work in a D&D context. I suppose one could call it a contrivance, but it also a lot more like the kinds of real connections people have in life.
But again, the ONLY time I really saw this was A) in my OA game (which never really caught fire, though we did play a decent number of sessions), and B) in my last campaign, which was far closer to narrativist, or maybe kind of neo-trad, its hard to say, but was definitely 'post trad'. Again, there's just nothing in the trad lexicon of D&D that really supports or encourages this sort of thing. Its a game which is designed from the ground up to be focused on rooms, corridors, battle fields, and monsters above all other things. Again, OA is a bit of an outlier here as the PLAYERS get to define (or at least roll up) stuff like their clan, their martial arts schools, etc.
I wouldn't say 3.x did much to change this, though it did add a bunch of character options, which created some mechanical potential. 4e really started to exploit it more, with the various builds and options PP, ED, etc. that directly referenced things like schools and whatnot. 5e is more mixed, there's not really much incentive or mechanisms to do stuff like this, but the options are there, background COULD be leveraged (though it seems sadly neglected) and there are some 4e-esque references to schools and whatnot that could be leveraged.
