A discussion about percentages chances, random and pseduo-random number series, and sample sizes probably isn't going to get much traction, is it?
Regardless, no, that isn't the only place to find better dev traits, and not everybody with a story will be any better than normal. But generally speaking, over time and larger sample sizes, drafting storied guys will give you a larger number of advanced dev traits than completely ignoring them.
More to the point, if the stories aren't ever generating, that means a lower overall number of higher dev traits going to the league at large, which has a negative impact on the overall franchise ecosystem after a few seasons. The stories actually cause the dev trait to increase from what it originally was (that is, if a story spawns for a guy that was a normal dev trait at the time the class was generated, and the dice come up favorably, his trait will change from what it was originally). If stories aren't spawning, the class overall has fewer high dev traits.
CPU teams starting to struggle with talent after a few years? Draft class editing cutting off story generation could be one of the reasons, especially since the CPU doesn't get the same in-season increase scenarios the player does.
So far as the weekly thing and stories disappearing, it IS a pain, and could be done better. In the interim, what I do is just check weekly, and make a pen-and-paper list of every guy with a positive story. If I'm not using my draft board for anything else (frequently the case given the way scouting currently works), I'll just throw them on there.
I don't draft those guys JUST because they have a story, but if I'm comparing two players that are roughly equivalent, and one has a story where the other one doesn't, I'll usually draft the storied guy just due to the higher
chance of a better dev trait.