Hiya!
Yup...but that just emphasizes my point: Feats and MC as
supposedly "Optional"...when, in fact, they really aren't for the seeming majority of Players (and DM's). Heck, when Adventurers League was being set up, that was one big question a lot (ok, person experience, but if so, then ALL DM's I know) were asking "Ok, so like...No Feats and No MC then, right? Because they are OPTIONAL in the core rules? Right?"... BLAM! Kick to the ballbearings!
For me, and pretty much every RPG'er I know, pretty much sighed and said "Ok then...so NOT OPTIONAL is what you're saying...".
Now, that said, I WOULD allow a Player to have his PC Multiclass...
if it made sense and the reason wasn't "to get more kewl powerzez an WIN!". You (collective you) all know when a Player is trying to pull off some kind of shenanigan's ...the little "DM tingle" that goes on in the nether regions of your brain that makes you squint your eyes a bit, pause, and think "Ok...do I call him/her on it right now...or not? ...if I'm wrong, I'm going to look like a controlling, paranoid D-Bag DM...". If I get that "tingle", then it's a hard No! Lucky for me though, my players are...uh... "less than keen on optimization min/maxing". They do put effort into being 'good' at something, don't get me wrong, but they will tend to err on the side of "Nope...that'd be too OP and stupid..." then go for the less-optimized choice 9/10 times. That 1/10 times they can't resist...tends to bite them in the buttocks sooner or later (it's called MIN/max for a reason!...

).
So, like you, the Player should make
some kind of honest effort to make a workable character...if given more or less "free reign" on character creation options/books.
^_^
Paul L. Ming