Right, if the odds on a particular turn are obviously less than 20%, how can the overall average value increase to 20%? It doesn't, because these are two separate questions and so have separate answers. Also, when you say "average to X%" you really need to understand that there's a bell curve involved. As I posted above, there's about a 95% likelihood that over 400 trials the results will be between 13 fumbles and 27 fumbles. The odds of 20 fumbles exactly is about 9.11%. This is because this question is a statistics question, not a probability question (the clue is "average," which probability doesn't do). Statistical analyses first build a model with specific assumptions and then give an answer that is based on the input data and those assumptions. Here, you're getting 20% as an answer but not examining how the model comes to that answer, or what extra information is being left out.
Um, did you read the post, because it spends the whole middle talking about multiple 1's per turn -- the entire analysis and how it works rests on detailing all the possible cases where a fumble occurs, especially multiple ones.
It's great to not want to deal with stats and prob -- they're a pain in the arse. But, if so, you should maybe stop asking how they work? Because, if you recall (and, if you don't, I quoted it in the prior post), you did ask how this works.
Regardless, the prob and stats of it all don't really impact your basic point, which I'd expand from fumbles unduly impacting multiple attacks to a statement that fumbles punish competence, period. You can be the best at what you do, in any field, and if you roll a fumble the usual expectation is that you make a major mistake. This means that, at a certain point of competence, you either succeed easily or majorly blunder -- you're either the hero or the goat. This can be true without fumbles, of course, if the GM is running with failures being due to incompetence, but it's magnified in any game that features fumbles because there has to be some delineation between routine failure and fumble failure, and that almost always comes at the cost of describing the PC's action outcomes as incompetent in some way.
I've taken a page out of Blades in the Dark, which tells GM to never narrate failure as a result of PC incompetence -- they are highly competent and this damages the fun. Instead, narrate failures as unexpected changes in the environment or due to the other side also being competent. This way, even when things don't go the PC's way, you're not making the player feel like their character is a blundering idiot when they're supposed to be a competent adventurer.