It's still NOT "story reasons." It's NOT "concept." The WHY of the argument to allow it is "so I can get X."
I don't think the 5e multiclassing rules are any bad, in fact they seem quite good for me.
But they are certainly unnecessary from the point of view of story or character concepts.
I don't think there is any character
concept that really needs multiclassing, not in an edition with 12 classes, 30+ subclasses, feats, backgrounds, and other variants.
I don't even think it's always a matter of grabbing abilities, because if you offer the player the option to gain any ability they want from another class in exchange for something equivalent, some players will still want to multiclass.
I think it goes deeper than that for some players, it might be that they are just eternally undecided on what they want to play, but they want to play it now...
Day one: I am a Fighter damn it! That's what the game is all about!
Day two: Oooo... look at all those cool spells, I am switching to Wizard!
Day three: Hey the Cleric is surprisingly the strongest class in this edition, how wouldn't you want to be one?
Day four: Enough with healing, I want to smash things, Bariarian!
Day five: I saw the light! Sweat, tears and charity, let's put ethics before everything, I'll be the best lawfullest Paladin evar!
Day six: Ethics are for wank'rs, an Assassin has much more fun.
Day nine: Hey I just saw the latest Batman movie, can I be Batman?
Day ten: You know what? I've never played a Bard... maybe this time... I could... perhaps... hell no!