"It" isn't suffering from those things. People who rely on them are.
One important thing to note here: I am expressing a preference and belief here. I am not declaring a truth. For me, increased uncertainty in die roll outcomes is net benefit when playing D&D (and other trad games). Unexpected results make the game better. Playing D&D with a set plot in mind -- like an AP -- or a set of rigid expectations -- "my character is going to take back the throne!" -- is less fun and creates a tension with the inherent randomness of play, which is a problem.
I think most of the push back you're getting in this thread isn't about your comparison of one way to play D&D compared to another. Instead, it's mostly about the below bit from your OP.
I have played and like some "story" games, but one thing many of them lack is uncertainty. Their mechanics tend to favor participants being able to say things that become true in the fiction (even if they don't call it that).
This is the main issue. That statement, combined with the title, certainly implies that you think D&D is better than those games. Which is fine as far as opinions go... but the logic used to support that opinion seems a bit shaky. Examples have been given of how story games do offer uncertainty in a variety of ways, and little has been offered to counter those examples.
I think even mentioning other games beyond different versions of D&D was not only unnecessary to your point, but actually contradictory to it.
I prefer when participants in D&D (and similar "trad" games) say what they would like to be the case, and then the dice decide how that turns out. That goes for the GM, too, btw -- the GM being subject to the same uncertainty is equally important in creating a truly surprising and novel experience.
So you prefer random generation of elements of play as much as possible? Again, a perfectly fine opinion, if I've understood correctly.
I can understand someone enjoying the elements of a random encounter... who/what is encountered, at what distance, with what starting disposition, and so on... over purely authored material of the sort found in modern day adventure path style games. I can see how that might be appealing more than a more curated approach.
But again, the snippet above... declaring actions and the dice determining what happens next... that description suits a whole swath of games that you're saying it doesn't.
As to which story games I was was thinking of when I wrote the OP, the one in my mind was Scum and Villainty. I know I will get push back on that because FitD games are "play to find out" but what I mean is that the actual dice system in S&V doesn't have much range and it usually requires a series of extreme results to created something truly unexpected since it all flows from the fiction (which is itself a constraint). But I did not want to get too deeply into that discussion because this thread is about D&D and how randomness impacts it. If you want to argue of about story games, start a new thread, please.
Talking solely about the range seems to miss the point of uncertainty. If a system is pass or fail, what does it really matter if we're using a d20 with a small range, or d100 with a big range? We still know it's either going to pass or fail. If the DC or TN is known, then there's not uncertainty... the odds are known. There can be surprise in the form of an unlikely result occurring, but that's pretty much true of any system that uses dice.
To say that because there are smaller numerical outcomes with Scum & Villainy means there is less uncertainty is odd. The game has, by default, three outcomes for its rolls. Three possible outcomes rather than two... more possible outcomes means more uncertainty. And this is without even getting into all the different options that the third result, success with complication, offers.
Again, I think if your point is just that versions of D&D that utilize more random generation offer something that's missing from more curated versions of D&D, sure, that's an interesting take. If that's what you wanted to discuss, then I think you did yourself a disservice by comparing D&D to story games because it doesn't seem like a take that you can effectively back up.