Hiya!
First off, I was just throwing out an example of what some DM might say/rationalise as a means of explaining why MC isn't around in his game. It wasn't my campaign, for the record.
Second, it wasn't exactly me who decided no MC'ing and no Feats...it was my players and I. Initially, first three 'mini campaigns', we were balls to the walls everything and the kitchen sink gaming with 5e. We wanted to get a solid "feel" for how 5e's system, and most popular (in our minds) options (MC and Feats) would fair with our style of play. Long story short...MC and Feats just were not something any of us really enjoyed. So, last campaign, the "serious this time...." one set in Greyhawk, at the first session I asked if we were going to use [insert small list of 5e options; MC, Feats, how healing works, how spell material components work, and maybe one or two more I can't recall at the moment]. Suffice it to say, MC, Feats, Healing 'system', and spell material components ("Spell Component Bag" // "Focus") got dropped, dropped, modified, modified, in order.
Anyway, on with the show!
Hiya.
No, it is not reasonable.
The reason that it is irrational has nothing to do with the contrived nature of the example situation; after all,
all of our made-up game worlds are contrived to a greater or lesser extent.
The reason it is irrational is because your example is of an irrational world, specifically: the inhabitants of the world are aware of the 5th edition game mechanics that control them!
No creature in-game can
rationally point to another creature and know that this creature is multiclassed! 'Multiclass' is a pure rules term and not perceivable in-game.
It's the equivalent of the Mayor of Utterley being tried and found guilty by the courts of having too many hit points for his level!
See above for the ''reasonable" explanation; it was just a quick example of what some DM may have for his world. Saying "it is irrational because...[reasons]" is a bit of an odd statement to me. What seems illogical for one persons campaign may be perfectly logical in another. For example, the fact that there are still hoards of dangerous orcs, goblins and kobolds anywhere *near* civilization in the Forgotten Realms is completely illogical. The "level" of NPC's in the realms makes heiring s group of newbie adventurers silly...just go get the city outriders to deal with it; chances are all of them are higher level than the PC's, better equipped, and better supported.
Again, different campaigns and play styles could easily have some means of 'everyone' knowing someones class, level, even HP's. I could come up with a lot of perfectly viable "reasons" as to why it is so on some particular material plane.
I think what this defense will come down to, however, is a persons individual idea of what constitutes a "class" or a "level". To some, a class is nothing more than a set of skills learned. To others its a persons entire being and outlook on life, death and the multiverse. A level could be a simple as a representation of time spent plying ones 'trade' (re: class)...and to another it could be a representation of deific favour, fate, and some nebulous 'hero factor' or 'destiny for greatness'.
At any rate, it always boils down to each individuals style of play. I'm not going to convince everyone that MC'ing in 5e is "bad" in it's current form, and it is highly unlikely for someone to convince me that MC'ing in 5e is perfect. All we can do on these forums...and all we should do...it present our own particular reasons and methods for handling RPG'ing stuff so that others can read it and maybe be inspired, or have them re-look at something, or otherwise stimulate thought. Maybe these boards need a separate forum devoted specifically to "DM Creative Ideas [non-rules focus]".

I'd be all over that like stink on an otyug! I absolutely
love reading about other DM's campaigns, ideas, and stories! I can spend hours and hours browsing Obsidian Portal (
www.obsidianportal.com, for those that don't know) and just reading about other folks campaigns. Mmmmmmm.....pure, freshly squeezed, imagination!
^_^
Paul L. Ming