I would argue the figure has more power these days. The more civilized we become and the more complex our society becomes, the more there is that desire to return to a simpler archetype of humanity and masculinity. We live in an age where brawn might seem less relevant (though I think that shows a lot of white collar bias as many jobs still rely on things like strength and athleticism). But we also live in an age where men are trying to look like Conan in greater numbers (just dip into weight lifting and bodybuilding circles, or go to a gym). I am not arguing this is all good. Some of it isn’t. One of my pet peeves at the gym is how common performance enhancing drugs and how abused legitimate treatments are so guys can put on mass. But it is there. I’d argue something like Conan is a much safer way for most guys to connect with this aspect of themselves. It is a vent, a cathartic power fantasy, the way action movies can be. And a I think a lot of men have a desire to tap into that. And there is always that tension between urban and rural which Conan embodies.
You're talking about something different then what I am. Of course fantasies of physical power and righteous violence haven't gone anywhere--they're basically the basis of most adventure fiction (and their appeal is hardly limited to men). What I'm talking about is the tension of civilized vs uncivilized as the theme of said violence. Spider-man punches people, but no one is ever like "then came Peter Parker, from the far-off land of Queens, New York, to crawl the spires of Manhattan with the mighty fingers he earned surviving that savage borough."
If you're not interested in that
particular power fantasy, you've got no reason to have an interest in Conan instead of the ten million other examples of adventure fiction where heroic figures enact righteous violence.
I've missed some of the intervening discussions but just pointing out that these same 'Conanesque' philosophies as you describe can be seen in characters like X-Mens Wolverine, Mad Max, Jason Mamoas Aquaman, John Wick or The Witcher - rightly or wrongly they remain popular tropes
Case in point--the only one of those characters who seems even slightly similar to Conan to me is Wolverine. Mad Max is an inverted Conan--he's
more civilized then anyone else in the wasteland (note the bit where he uses the knowledge of first aid that he was trained in when he was
in the police to save Furiosa). The DCEU Aquaman is doing the sword-in-the-stone thing, the man raised in obscurity who turns out to be the true king, which is a totally different trope. John Wick is the best assassin from a society of assassins. Geralt is a Witcher, a position society relies on to protect them from uncivilized monsters, even if they don't necessarily like it.
Wolverine
is Conan-like, in that his wildness, his berserker rage and feral instincts, are positioned as giving him advantages the other X-Men don't have. But he's a much weaker example then Conan himself, as is Jack Reacher. My point isn't that this fantasy is entirely gone, but that it holds much less appeal in the modern day then it once did.