So you imagine a sword that is looking for a "haughty and snobby knight" with a lot of breeding, or shall I say inbreeding, to wield it!
I would say the nobles of a fantasy world are more likely to have the magic that flows in the bloodline story going on than the realistic one as in their world dragons and gods and so on really did interbreed in the not so distant past - and the rest of what you say is too realistic
And you said they would want someone whose mind they could overwhelm didnt you? if they did get one of those foppish well place nobles that might be the prize -> an ego easily consumed and a kingdom to do their bidding. It might well be the most likely result.
Literarily : Stormbringer discovering that a strong mind able to resist it made it able to defeat its brother basically in act of cooperation could also be an oddity. Elric's somewhat weaker minded and more evil cousin was a less desired wielder. Elric was atypical and seen of weak blood by his peers (but realistically he was exactly not inbred - your nod to realism) but even his physical weakness was something he was able to overcome effectively with a combination of mental and physical effort ie he had to work to be as awesome as he was the second greatest swordsman of the land and the greatest ritualist and perhaps most educated individual on his world knowing many languages with many libraries of resources at his disposal, who rediscovers the secrets of fast casting magic intuitively before Stormbringer even encountered him.
In King Arthurs story we also get someone who is still raised by in part by warrior class characters just lower echelons and partly by the Bards of old ie he was raised in the classic way of heros partly by historians again an instance of unusual degree of education making a hero strong which appeals to modern sensibility. Considering Excalibur a sentient sword is definitely not a given though sometimes we do see that transformation happening in various retelling of the story.
Here are some issues with the other side : The typical peasant never traveled more than 20 miles from their home (inbreeding isnt solely the providence of nobility) and rarely has time to do or learn much beyond what is needed for survival he relies on the fighting class, doesnt have training in use of weapons to speak of especially not the sword, he might be more likeable than that foppish noble you picture but he probably doesnt have the desire or social power to even keep the weapon. Depending on where and when he lives it may be illegal for him to even have it. But even if not exactly illegal it is a tool his overlords will want and one less useful than many or the money he could sell it for. I think it is fairly certain a exceptional weapon lusually would end up in the hands of the fighting class (aka lesser nobility very fast).
The reality is a lot of these noble houses started out as warlords, such as William the Conqueror, the only reason William was "The Conqueror" was because he was a good organizer of men, he won battles, and thus defeated King Harold of Britain.
One could argue the cycle between those who earn their rulership in war and those who fall into impoverished capability, was still entirely within a group/class that was directly engaged in and trained in war up until modern times.
And very likely even the Arthur vaguely of history was just a warlord too and only made king in legend.
Yes people imagined the strong personalities would be inherited but not having to work to achieve what you gain has an impact on motivation and never being without seems to result in impoverished empathy all too often (there have even been scientific studies confirming this at least as a tendency)
Realism results in the rejection of myth, legend and literature.
