This is how it has always worked, fudging rolls as a DM comes very naturally and even first-time DMs in their first sessions realize it's needed and start doing it.
These might be the two worst arguments I've ever seen together in my entire life in any discussion ever. "This is how it has always worked" and "first-time DMs in their first sessions start doing it" don't work here exactly like they don't work in any discussion ever. If we stick to "this is how it has always worked", we would have dwarf and elf as classes and not races (I mean, giant incline, but I don't think you would agree to that). If we stick to "first-time DMs in their first sessions start doing it" we would have all kinds of abhorrent rules, like "you can cover yourself in shields to gain infinite AC" and "triple 20 is an instant killing blow without any chance of surviving".
At best, those two aren't arguments at all; at worst, they are arguments in favor of doing the opposite.
It's not only for a better story, it's also to prevent level 1s from dying in their first encounter, or to prevent the session from being bogged down in a single fight for an hour and a half. A friend of mine and I concocted a one-shot the other day for one of his groups, and they couldn't finish it in time because the players had terrible rolls (like a 1 and 2 on a roll with advantage) against a coral golem and it lasted like an hour and a half. That shouldn't really happen.
That should happen, and you should be able to make that fun. Players could retreat, regroup, and plan a new assault on the creature, or one of the characters could die, giving to the surviving heroes a new reason to defeat the villain responsible for the death of their companion.
I see mainly two problems in your approach:
- first, you take for granted that you know what's best for the players and the adventure. You are basically saying that you know better than the rest of the group how they should have fun with the game, but that's not necessarily true. You should ask the players how they would like to play: if they prefer a more narrative approach were they don't want to risk losing their character, then everyone could agree that the DM should fudge rolls in certain situations (even though there still are better solutions, like playing with "fate points" or finding ways to keep playing with bad rolls: for example, a bad roll might mean that you still get to hit your enemy, but killing him wasn't a good idea after all, because the soul of an ancient demon was bound to his life. "Failing forward" is almost always better than fudging rolls).
- you are playing just to see the players experience the story you concocted. That's not what the game is supposed to be, or, at least, that's not always the most fun way to play the game. The players have no way to actually influence the story with their successes or failures, because you always decides what's the outcome of their adventure. What's the point of rolling that Deception check if it was already decided that the guard had to believe my words? What's the point of rolling my attack roll if it was already decided that the bugbear had to die? You are just deceiving your players.
Fudging rolls to never have to come up with alternatives to the story you planned out is just plain lazy. Come up with creative solutions, create the story with your players instead of imposing your fantasies on them.