Two Three ways and it happens often
- As you said. A cumbersome and complex resolution system
- as you said games like FATAL
- A system of where the bonuses and dice are not obvious, causing confusion and hindrance.
- Happens when skills and bonuses aren't clear. What's a Heart check? Can I add my Guts modifier to this?
- A unbalanced system of bonuses compared to the obstacles expected in frequency or power
- D&D 5e got better but there used to be a bunch of super skills as well as a bunch of niche skills
- D&D's ability scores/mods have only grown in power but the imbalance between them is never dealt with, leaving it up to the DM to discourage having a bunch of Dex/Cha strikers.
I don't really see the difference between #1 and #2. Cumbersome and complex is how I would describe a game where it is sufficiently unclear that you don't actually know how to use it.
And I would argue #3 is still a problem for 5e on both of its prongs. Niche skills include Investigation (which is poorly-understood, difficult to use, and rarely necessary), Animal Handling (often redundant with Nature, and rarely useful overall), Survival (most of its listed tasks can also be done with some other skill, mostly Perception or Nature), and Performance (almost completely useless). Athletics and Sleight of Hand are both in danger of falling into that category as well, only saved by having very basic utility value. Super skills include Perception, Persuasion, Stealth, Deception, and to a lesser extent due to being context-specific, Nature, Medicine, and Insight.
4e actually took steps (in an exception-based way) to address the gaps between the various abilities. 5e threw that out the window, and the rather weak effort to make all six stats into saves did not even remotely address the gap. Dexterity is still the top stat, followed by Wis and Con, unless you're a Charisma caster, then Cha probably fits between Dex and Wis/Con.
So, I guess then what I'm saying is...it seems like, if 5e is so good at that "give me a Wisdom roll" process, despite being plagued by some of the very problems you mentioned here, I'm not really sure how any game that isn't really,
really badly designed would not also do this.
E.g. I've played SR5e and W20, and both of those games have nigh-identical, very straightforward mechanics for such rolls. In W20, you add your Attribute (ability score, a number of dots usually from 1-5) to a relevant Ability (which includes both "skills" and other stuff, again usually dots but 0-5), and then roll that many d10s, target number is usually 6-7. Add up stuff at or above TN, subtract off the 1s. If it's positive, you succeeded. Easy-peasy. Shadowrun works very similarly, making a dice pool from your attributes + relevant skill, but uses d6, TN is 5 or 6, and 1s don't
subtract success, they just make complications if there are lots of them (
nasty complications if you also fail the roll.)
Obviously, dice-pool systems differ from single-die systems, but overall the effect seems the same. Tally up your bonus, roll the dice, check if you succeeded, move on with your day. If the system is even merely competently designed, I don't see how the original statement doesn't apply.