One of the things I like about 5th edition is the inclusion of backgrounds which I (naively) thought would eliminate some of the desire for people to multiclass. After all, does my Fighter really need to take a level of Rogue in order for me to meet my vision of a character with who grew up as a gutter snipe stealing things? Or am I just better having the Criminal background which will allow me access to some skills and proficiency in thieve's tools?
That was a naive belief on your part, yes, because you are not looking at multiclassing the way other people are looking at it. Since you expect others to bring the same perspective, you are thus blindsided when they want something alien to that perspective. That is, you appear to see "multiclassing" as serving one, and only one, valid purpose: to reflect historical background of a character, or provide mechanical support to something already established about a character's story.
There are at least three other purposes for multiclassing. One, as has already been brought up (because it
always will be, usually in the most derisive and often mocking manner possible), is multiclassing for "optimization." Despite the demonization this gets,
most players consider some amount of optimization in whatever they do. This is why they scratch their heads at the fact that the 5e Trident is a "worse" spear (heavier, more expensive, higher training required, but otherwise mechanically identical.) It's why you don't bother casting
sleep at high levels, because it just can't do enough to be worth using. Etc. Unfortunately, what people always hold up is the
worst examples of such behavior, as though that is the only and inherent result of optimization, while ignoring the degenerate behaviors that other interests can foster (the classic "It's what my character would do" excuse, for example, or the "joke" character that is mostly a drag on the party.)
But I said there were (at least) three. The second is multiclassing for archetype, rather than for identity/history. 5e has
somewhat reduced this burden through a smattering of subclasses, but whether they're actually
good at representing those archetypes is hugely variable. Some are pretty solid, e.g. the Shadow Monk is IMO a great way to represent a ninja-type character. Others are imperfect but serviceable, e.g. most of the ways to be a "swordmage" are either "
SWORDmage" or "
swordMAGE," failing to truly integrate the parts into something harmonious and more-or-less equal. And others still are just crap, e.g. if you want to play a Warlord in 5e, your options are Battle Master (not actually a Warlord...), PDK (
garbage), Mastermind (really not very good
and not actually a Warlord), or
something magical (emphatically not a Warlord.) With a lot of multiclassing, you can kludge together something vaguely Warlord-like, but if you're forced to stick to just subclasses and feats, you're SOL.
Third, there is multiclassing for
future story, which is something I've done. Wishing to explore a certain kind of story with a character and refusing to take Warlock levels because that would conflict with that, but (say) Bard levels would make total sense. Or to represent intentionally having a character practice new skills and methods that they did not use before. My "can a character get every skill proficiency?" exploration hinged critically on what kind of story I could tell about such a person, why they would
seek out knowledge of all the skills, and thus shows a blend of both optimization (trying to get the maximum amount of something),
Admittedly I grew to hate multiclassing during 3rd edition. Largely beacuse of the way prestige classes worked. In my mind, they took away all spontaneity requiring players to plan ahead to select specific classes and feats in order to get the prestige class instead of choosing such things in response to the events of the game. And as a general rule, I just don't like keeping track of character builds by dipping into other classes. But I recognize that some people just love building characters and multiclassing can be a part of it and there's nothing wrong with that.
I certainly agree that PrCs failed at what they were intended to be, and instead became meticulous "build everything perfectly before session 0" fodder for optimization of the worst sort. That was the fault of the designers, not the mechanic, but the damage is done and I get why that leaves a permanent distaste in many folks' mouths. The thing is, they
also contributed to an awful lot of bad MCing for poor reasons as well: people pursuing quirky franken-characters because "it's what my character would do" (even if it means being dead weight for the other players to drag around) or because one is chasing a...shall we say, idiosyncratic and self-promoting story.
I hear multiclassing is optional, but I've never met a player who viewed it as optional. Does everyone allow mutliclassing in their games? I don't like it, but I've never restricted it.
I personally dislike perfectly functional, non-exploitative options being banned outright. The only things I dislike more are fudging and
pretending you allow everything while
functionally banning things outright. So, if someone up-front says multiclassing is banned, that's a red flag for me.