OK. I can buy that... But the other very good explanation I've heard for pattern stall-spin accidents is this: First, that it's much harder to recover from a skidded spin entry, and that many/most CFIs tell students to limit their bank angle to 20 or 30 degrees in the pattern (to avoid an accelerated stall, but there's often no mention of that) and then when someone inevitably overshoots final, they get to their bank angle limit and try to tighten up the turn with rudder and elevator so they don't "bank too much" and boom... And that, IMO, is a result of bad training. WHY is it a bad idea to go to a higher bank angle when turning final, WHY might it be a bad idea to overshoot final in some situations (such as parallel runways), WHY a skidding turn is an even worse idea, HOW to recover from mistakes made on base in the safest way possible... All must be taught, and if they are properly taught in a way that makes them memorable, that student will be among the group that recognizes things before they put all the links in the chain.
Even for the task saturation scenario you describe, I think training people to ignore pax at critical stages (and brief them so they're less likely to be a problem in the first place), and if they get to the point of feeling saturated that maybe going around early is a better way to deal with it than continuing the approach to the point of a loss of control. Sure, it can still happen, but one good memorable flight lesson can have a big impact.
Fuel exhaustion, definitely poor ADM... And I'm sure every CFI talks about it, and every DPE is testing on it. I think two things that would help this are to practice deviating from a plan, and to learn how to fuel an airplane at a self serve pump. It seems like get-there-itis and the type-A "Plan A is the only plan" personalities can be problematic, but there seem to be far too many people who fly past airports with 24-hour self serve fuel only to crash short of their destination, and I think a lot of that is that they have no experience with, nor clue about, how to fuel an airplane themselves.
For high DA, well, it's only talked about. It really needs to be experienced. Throw another person or two in the back seat, maybe some ballast to get up to MGW, and take it up to 8, 10, 12 thousand feet. Simulate a takeoff from a high elevation airfield, with a minimum climb gradient. That kind of thing isn't done.
For IMC, some of it is likely caused by "plan A all the way" type thinking and that could also benefit from practicing deviations. I don't think anyone flies into a cloud they can see from miles away on purpose, they likely are getting sucked in by things getting a little worse but "It looks like it might be better ahead" and just continuing into a situation until it becomes unrecoverable. Personal minimums are definitely talked about during training, but I think in a fashion that's a bit too simplistic. If you make a personal minimum of "3000 AGL ceiling" that's hard and fast, you run into "Well, I'm only flying to that airport 20 miles away, 2500 feet is plenty" and it becomes a normalization of deviance thing. A FRAT is probably a better idea, but that's a lot harder to explain and implement and there's plenty of CFIs out there who have never seen one themselves.
So, there's certainly training that *can* be done. It's a matter of accomplishing it in such a way that it doesn't add too much extra cost yet is effective and memorable.