because they are about character / class design, not worldbuilding. You cannot have martials barely competent enough to use every fourth weapon they find next to D&D casters. Heck, I am not even sure you should have the current ones next to the current casters...
The background features are about character design, not about worldbuilding. There's not a single part of any of them that's about worldbuilding--to quote
you, if you say they do, then your interpretation of them is wrong and does not align with their intent.
And you certainly
can have martials not able to use just any weapon they want. Back in AD&D, at least in 2e, there were weapon proficiencies that did indeed limit the number of weapons a fighter could use well. You could easily say that a 5e/5.5e martial starts out being proficient in a number of weapons equal to, say, 6 or 8 + their Int mod, plus more as they level up, and that would certainly be fair and give them plenty of options. Or that the class gives some weapon proficiencies and the background or culture gives others. If you're the DM, you could ensure that most of the magic weapons they find are ones they can use, if you felt like it, so they're not "barely competent."
Am I saying D&D should do this? No. But if you
actually care about the game's logic, then
this should be a much bigger red flag than a background feature that you and others claim is rarely used in the first place and can be justified with in-game reasons.
(Also, spellcasters
can't just use any spell they want. They're limited by class list first, and then, only clerics and druids can cast any spell on their list--the others are limited by what the number of spells they can learn or by what they can write in their spellbook--and other than the two free spells a wizard gets each level, the DM controls what spells a wizard can find.