As a DM, I have fudged rolls. It tends to be in low-stakes situations. When a PC caster threw down an AoE spell on a roomful of mooks and, against all odds, all of them saved, I changed a few to failing. It didn't save the PCs or doom the mooks -- there was no real danger to the PCs at that point, the mooks weren't going to survive two rounds of combat anyway, reduced the grind of taking out everyone individually, and made that 3rd level spell slot not a total waste.
I have made intentionally questionable tactical decisions on behalf of monsters that were steamrolling the PCs to avoid kills and TPKs, but those poor tactics aren't fun and suck the fun out of the game (for everyone) faster than fudging a few die rolls, so I won't do that again (unless I screw up and do it again, in which case I'll feel bad about it again).
I'm not currently running a game, but when I do, I might empower the in-game pseudo-fudge powers -- inspiration, bardic combat inspiration and cutting words, the lucky feat, legendary resistance, etc. -- to be more flexible and fill the niche of fudged dice rolls. Giving monsters and PCs extra abilities to use reactions to re-roll is another option.
And I absolutely and unapologetically curate random encounter and rumor tables. Usually I don't roll at all, but if I'm rolling to help me decide, I still reserve the right to veto any roll that has an unappealing result.
After reading this thread, I will definitely talk to the group during the game prep phase to tell them explicitly what I might do with the dice.