I think most games build their skill probabilities under one of two assumptions:
A. Skills are like combat, and represent things that need a roll under pressure.
B. Skills are a separate thing, and are meant to represent anything you do but the most trivial thing. With possibly separating combat, magic, or other items out under a system more like A.
In the first, the GM is supposed to let people succeed on things they should be able to do when there is no pressure. In the latter, the skills often have wide ranges of both checks and modifiers, such that auto fail and auto succeed is built into the system.
I think either can work just fine, given the tastes of different players. If what you want is the high excitement, then there really is no need for B. It's just extra complication getting in the way of getting to the next roll that might fail. Whereas if you want the game to be more about the mundane successes building up to something more slowly but inexorably by using the abilities of your character, then A can start to seem a little lacking. It's taste.
What I don't like is a system that tries to have it both ways, but then the writer of the system doesn't put the work in. This is yet another time to point out why the 3.* craft system sucks, by the way. You could sum up a chunk of the 4E and then 5E improvements to WotC D&D as "realized that they had a lot of things attempting style B game poorly and then made the design decision to rip them out root and branch."
A big part of my current home design is trying to bridge that gap intelligently, and give the GM and players tools to manage the distinction. Part of the solution is that skills have a "tier" rating, such as "Novice" or "Expert", and also have mechanical underpinnings. The distinction between 4 success layers (fumble, failure, success, and critical) works into it as well, but making "failure" mean something different in tension versus non-tension checks. Basically, an "Expert" has to fumble (which is very unlikely) in a sustained piece of work requiring multiple checks to fail pulling off an expert-level task. And even if he does fumble, he's well equipped to deal with it and succeed eventually (not being under pressure). A group of lesser beings can attempt it, but the cumulative chance of one of them fumbling and blowing the whole thing is likely, making such attempts the domain of the desperate only. If no one gets seriously hurt, they can keep trying, but it is likely to be beating their heads against the wall. It also helps mechanically that I've built in group dynamics from the ground up, instead of tacking them on after the fact. Or the GM can rule on it, because the math of the system backs up the likely outcomes anyway, thus saving the hassle for those rare moments when desperate outcomes and no immediate tension actually matter.
Whereas for simpler checks under pressure, the Expert still has a notable edge, but the game assumes that the tension of the moment narrows the gap. If you are bleeding out on the icy ledge while the yetis attack, you'd rather have the expert healer, but you'll settle for the two mountain climbers with first aid if that's all you can get right now. Whether such a system would appeal to others, I don't know, but it at least is mechanically supporting the design goals.