Right, but that’s something all games do. They all involve fiction where the GM can place narrative pressure in different ways.
So that’s not unique to 5E.
So what? What does how another game does the thing have to do with giving advice to a DM on doing that thing in their D&D campaign? Other than providing inspiration, absolutely nothing.
Hit dice are so connected to hit points as to be nearly the same thing.
Okay. Look at how I worded that part of my post. I am grouping them together. Not sure why you’re saying this as if in counter to my post.
I don’t entirely agree about spells, though. Yes, they are a resource that needs to be managed, and they create decision points for the players and so they can be an engaging part of the game.
And they create pressure when they run low, because pet of your team is markedly less effective now. Even just running low with the end of the action not clearly in sight is stressful.
But with the exception of low level characters who have few slots, are most casters burning through all their spells without engaging in combat? What are they using that many spells on?
With the exception of very high level characters, yes, and all kinds of stuff. Like, spellcasters cast spells in damn near every scene.
It’s all designed around the expectation of a certain number of encounters per day. All the resource management that’s meaningful in 5E goes back to that.
Capers have encounters.
if you like the GM creating these kinds of things ad hoc and running with it, if you trust your GM to do so and do so well, then AWESOME! This is great. The problem comes in not in that you cannot get a good outcome for a heist in 5e, but that any such outcome is entirely a product of your table and your GM. 5e does not help you.
It does help you, by providing the tools to adjudicate play and then getting out of the way. This isn’t your preference, and that’s fine.
If this claim is true - that D&D 5e can do heists just fine - then what RPG can't do heists just fine?
Who cares? What does Fate’s ability to do capers have to do with giving a DM advice about doing a caper in their D&D campaign?
It doesn't seem to tell us anything about whether or not the character should do better in a cooking competition than another character without the feat. That would be something the GM would just have to decide, I guess.
Cooking Utensils. Proficiency. Proficiency increases the average d20 result when performing tasks using the relevant proficiency. What are you not getting, here? 5e even has rules specific to opposed ability checks, and a pretty clear framework in downtime activities (especially in Xanathar’s) if you want to have the PC roll against a variable DC that represents how well the other contestants did, instead. You set a DC by rolling a couple dice, usually 2d10, though some activities have a set DC (crime has a scale in increments of 5) and adding a number or not depending on how hard you want things. The PC then rolls 3 different checks. To do a solo caper in your downtime, it’s Stealth, Thieves Tools, and PCs choice of Investigate, Perception, or Deception.
It’s a good framework, though newer DMs would benefit from having the moving parts of the framework explained rather than just being given examples.
So, 5e has several ways to run a cooking competition, but they’ll all involve making a check with cooking utensils, which means that someone trained in them will do better than someone not trained in them.
But unlike both D&D and other PbtA games, in Blades you can resist the consequences (which, depending on where your game is on a sliding scale between Ocean's 11 and Lock, Stock and Two Smoking Barrels, may be either negating it entirely or reducing it) and have an ability to make a complication into a benefit.
That dynamic is great, and I’ve used it in D&D because it can be used entirely as a narrative “running the game” thing rather than a mechanical framework, or it can be tied to a limited resource that exists in the game already, and I’ve done both for different situations, but it isn’t a requirement of running a caper.
I guess if 5e D&D is not special, then either (i) no one can ever talk meaningfully about any RPG being better than any other, or (ii) it must be possible for some RPGs to be better than others (in general? at this specific thing? for this particular purpose?) in which case the OP is wrong.

The OP never claimed that it isn’t possible for one game to be better than another.
It's worth noting that OPs original complaint was against tone-deaf advice. Which no one is in favor of.
And yet several people in this thread have given such advice in other threads.
At least one person literally ranted at me that I’m a bad person for suggesting that it isn’t a waste of time to do a caper in D&D .