Well, because I'm not sold the other methods are actually less contraversial; they're just less traditional so there's less focus on them.
"Say yes or roll the dice" is one of the most traditional pieces of advice there is. Saying yes (or, sometimes, saying no) means you don't invoke the mechanics in the first place, so there's no need to fudge. That's what would cover "calling a fight" type situations, where the DM basically just straight-up says "alright, you guys have won." (I am
assuming that DMs wouldn't "call" fights against the party, as that's kind of a jerk move.)
Apart from that, what could be controversial about "be diegetic"?
(I'm assuming you're not including various baked in mechanical tools here; if you are, we're having slightly different conversations at the moment, but even some of those are distinctly things some people react badly to).
I suppose that depends on whether you define "say yes(/no) or roll the dice" and "be diegetic" as baked-in or not.
Well there are a number of things:
1. Speed. Fudge the die roll now and avoid that result right now. Make a note of it, make sure it doesn't happen again if you need to, but, instead of insisting that this die roll stands and derails the session for the next hour (for whatever reason), change the result and move on.
I find this hard to process. If the DM can improvise new diegetic situations when a die roll is not in question and do so quickly enough to not derail the session, what prevents them from doing so when a die roll
is in question? That is, if the DM can seamlessly and speedily extemporize about the Queen's response to Garka the dwarf barbarian being unexpectedly articulate when she expected a huge boor, I don't understand how they shouldn't be able to seamlessly and speedily extemporize about (to use my previous example, possibly from a different thread) the Greater Shadow exploiting its powers over life-energy to save itself from an unexpectedly potent assault by the PCs (or whatever).
2. Mistake. The DM called for a die roll without thinking of the consequences beforehand. We've all done that. Yeah, make this check... oh, you rolled really badly.... err.... ummm....

Basically just a mulligan for something that probably shouldn't have been rolled for in the first place.
For my part, I see this as
even more important than being honest with the players: it's being honest with
yourself. DMs cannot live up to a standard of never being able to make mistakes or do something wrong. That's not healthy for them, and it leads to unhealthy expectations from the players. Much better to say, "Aw, beans, y'know I really shouldn't have asked for that roll. Ignore that--instead <stuff.>" I have said this a few times in my own game, where I reflexively asked for a roll only to realize that there were no interesting consequences for failure. Admitting those mistakes has not ruined my game, and has in fact helped my players understand where I'm coming from.
3. The results don't make sense in context. Granted, this is probably a really corner case one, but, it does happen. Particularly if you're using things like Critical Hit tables - how exactly did you cut that guy's arm off with a hammer? Let's reroll that one.
I see this as either just a variant of the previous, or an exercise in interesting challenge: how DO we make sense of it? If no sense can be made of it
whatsoever, then we should admit it, e.g. "oh...you rolled to decapitate it but uh...this thing
doesn't have a head. Reroll that until you get something other than 9, since that doesn't make sense." But if some sense
can be made of it, even if it requires some leaps of logic, roll with it! Or, perhaps, ask the players what they think, e.g.:
DM: "Hmmm...a stone golem doesn't really have a 'head' in the usual sense. Charity, what does happen when you strike this thing with your vorpal sword?"
Charity: "The sword may not know what 'golem' means, but it does know what's the most important part of an opponent. As I thrust the blade into the golem, its heart is not pierced, but driven out through the golem's back."
DM: "Ooh, I like that. It falls to the floor with an unusually dull thump, glowing softly. You've slain the golem, and now have an intact golem heart!"
I've had an enormous amount of super cool stuff come from me asking a player to explain how something happened or why it made sense in context. Even with a player who is both shy and brand-new to TTRPGs.