Very generous of you!TI meant being fair as in even-handed with how I treat players - no favoritism. I would lump problems and situations in with challenges, but your points are well made and better crafted than mine.
Riffing off your idea of even-handedness, here's a question: if the GM is coming up with a dungeon, or a scenario, or a situation, should s/he have regard to the details of the players' PCs?
I want to say that in classic dungeon-crawling D&D the default answer is "no". Part of the challenge for players in that game is to use the resources they bring to help "beat" the dungeon, and also to recruit into the party (as extra PCs, as NPCs/henchmen, or whatever) the skill sets that they need but don't have.
I'm not saying that you should never have a deliberately PC-targetted dungeon in classic D&D play, but it's not the default.
But to go to a different end of this particular spectrum, setting up a situation in my Prince Valiant game, or my Burning Wheel game, is all about knowing who the PCs are and how they fit into the gameworld. In Prinve Valiant - which is pretty lighthearted - this is about broad tropes/stereotypes: eg in our last session two new PCs, an itinerant entertainer and a squire who is the sone of an urban merchant family joined with the two estabished PC knights, who were themselves down on their luck. So the initial scene was established so that it made sense for the two knights to come to a town's market square where they could cross paths with the entertainer and, in due course, the squire.
Burning Wheel is more gritty and intense than Prince Valiant, and the degree of "personalisation" is correspondingly higher: it's all about pushing these PCs (as they read on the sheet and as they are played by the character) in these ways.
To start a session of one of these games with something that was devised "neutrally" or independently of the GM's knowledge of the PCs would be a wrong move.
I think our RPGing community, and our conversations about RPGing, will become more vibrant and more robust when we really think about the diversity of our games (across tables, but also at tables as we rotate through different systems and different sorts of approach) rather than trying to fit everything into really narrow and doctrinaire compartments.