In a game where failure is part of the fun, there's no need to fudge.
D&D - in my opinion - doesn't do a very good job of making failure fun. I'm not talking about the hilarity of absolute catastrophic failure, or those meat grinders you used to run where everyone came with a pre-rolled four pack of victims, but rather that miserable drip feed of mediocre rolls that leaves a player feeling utterly pointless. They soldier on as their supposedly competent hero whiffs every round, not complaining but also plainly not enjoying themself. They don't chuck their toys, but they are disheartened.
This is a really interesting and important point, imo. I can't speak for everyone, but I think some systems and their stated or implied play styles might unintentionally encourage fudging, because they don't have stuff like mechanics or guidance for failing forward. If the consequences of failure (and success, for that matter) are cut and dry, it's hard to turn bad luck into something fun.
For example, if you roll a critical success when hitting someone in D&D, it's pretty clear what happens--there are rules about extra damage and even feats that rely on a crit. And in a lot of games a critical failure is presented as a fumble--the PC doesn't just fail, they screw up in epic, often embarrassing fashion. But if you roll a miss in most PbtA games, you don't necessarily do a pratfall while also failing. The guidance is often that something bad but unrelated to your own prowess might happen--a friendly NPC takes the hit for you, or while you're circling your opponent you hear enemy cavalry approaching. You can even potentially succeed while some new consequence takes effect--you might finish off a wounded enemy, but you do it with such brutality that nearby NPCs (and maybe PCs) are disgusted and frightened by you in the long term.
PbtA is basically defined (imo) by tons of fun failures. In 5e, something like that disgust-inducing kill would be mechanically possible--you'd roll a 1, and you'd just miss.
Anyway, I'm not advocating for PbtA over 5e in all things, but I do think systems create unintended consequences (including the single d20's lack of curve, making even supposedly competent characters take nothing but wild swings). My preference is for games with rules like what you're describing, where players have some metacurrency for big, meaningful rolls. Lots of great tension there, as they decide when to spend and when to save.