Because some people don't like it. Again, they aren't required to share your views that's functionally the same. I can pretty much promise you if you unpack that there will be people in this thread who will find it unacceptable.
There's a pretty big gap between "some people find X dampens their fun, so they would rather it never happens in their game" and "X is so controversial for some folks that it will almost guarantee an argument if discovered, and has a very high chance of damaging the group." Don't try to paint all these things as though they are the same, or just slight variations. They aren't.
Call it unhealthy if you want (I think that's a pretty harsh characterization, but not my job to tell you how to see things), its still the practical reality of how some people want it done.
All expectations of unremitting perfection in performance are unhealthy. Human beings are not capable of performing without error 100% of the time. Mistakes can and will happen. I don't see how this is an extreme position: don't expect your DMs to be perfect, and don't lead others to believe you are perfect as DM. This isn't rocket science.
I find it hard to see fudging as anything other than the GM making the decisions while pretending that the dice are taking some of the responsibility.
Yeah, there's certainly an undercurrent of that.
I suspect many of us (even firm anti-fudgers like myself) might agree that a GM changing a random encounter roll is not really fudging, as it's not so much a part of the resolution system as a means of giving the GM ideas (YMMV). Encounter tables are in the GM's domain.
Yeah, I have no inherent problem with "hey dice, give me an idea. [roll] No, dice, give me a GOOD idea." Particularly when, as you say, the tables are not something the players could even in principle have knowledge of. If the point is simply to spur on DM creativity when the well of improvisations has run dry, then the roll has no effect on player agency nor their ability to learn to play the game. Though even then I still VASTLY, OVERWHEMLINGLY prefer not disregarding rolls. I just wouldn't be upset if someone else chose to do that.
Where we disagree is in the middle - combat and general skill resolution. Are the dice and associated resolution mechanisms just a suggestion, a way of giving the GM ideas that they can then choose to override? Or are they outside the GM's control, not so much in the players' sphere as no-one's sphere, a kind of no mans land where the outcome is neutrally determined?
The latter. That's what they're for. They provide a truly neutral arbiter, incapable of bias or favoritism, assuming the dice are fair and not weighted. If I don't like possible outcomes, I as DM have the power to change them. If there are no actual costs for failure, the dice shouldn't be involved. If I have invoked the dice when I should not have, it's literally as easy as "oh, y'know what, you just succeed, forget about the roll." That kind of statement should not be even the slightest bit controversial and accomplishes the exact same goal. (Likewise the closely related "calling the fight" stuff: there's no fudging involved, because you are openly skipping the invocation of the mechanic, which is a perfectly legitimate thing to do.)
Learning how to set the outcomes so you are comfortable with all the results is a vital DMing skill. Fudging is a crutch to avoid needing to learn that skill, and is not even necessary for correcting any errors that crop up. It is always within the DM's power to address any such errors diegetically, and in so doing, creating new hooks and opportunities. None of the controversy (since some amount of diegesis is essential to all forms of roleplay, that's literally the thing that makes it not merely numbers on a spreadsheet), all the benefit.