Hiya!
In my game, I've never had a player MC his character since we started playing about a year ago. Actually, I've never had a player even
consider a MC character for more than about 3 seconds...and that was only recently, one time.
The problem my group and I have with MC'ing since 3.x days is that you are "never multi-class". You are a guy with two classes (or three, or whatever). You aren't a Fighter/Magic-User...you are a Fighter and a Magic-User. You aren't a Cleric/Thief...you are a Cleric and a Thief. It's hard to really explain what I mean.
In 1e, you could be a Fighter/MU/Cleric...you'd be 1/1/1. As you gained XP, you generally divided that XP evenly, but it didnt' have to be. If the DM felt you did nothing but Fight, only casting Cure Light Wounds once (no other cleric spell, no turning undead, no MU spells or magic item use, etc), the DM generally made you put more into Fighter (so if you got 500xp he might make you put 400xp into Fighter, 75xp into Cleric and 25xp into MU).
In 5e, the very first time you play your character...you are
ONE CLASS. Period. Even if you 'want' to play a Fighter/Wizard. Your characters background story and all that will have ZERO effect on your actual capabilities as far as Wizard goes. You can't really have a bg that has your characters father as an accomplished warrior who taught you the dance of steel every other day, and have a mother Magic User who always dragged you away from your work out to teach you the ways of magic...both parents vying for your affection and time. When the DM says "You are all in a bar...", and you all introduce yourselves, you are stuck with "I'm a Fighter". You can't say "I'm a F/MU", because you
aren't. As you gain XP, eventually you will hit 'next level'. At that point you have to decide which class you want to advance in. This gives the feeling that all the fighting or all the casting you had done for the last half-dozen sessions is useless; you didn't learn a dang thing in that class. So...you were really "never a Fighter" if you advance as a MU, and you were never "really a MU" if you advance as a Fighter. If you did/were...surely you would have learned
something, right? Nope. One or the other.
This disconnect between character, actions/rp, and mechanics has pretty much made the 3.x/PF/4e and now 5e "multiclassing" a bust for us. In the immortal words of Mr.Horse..."Hmmm....hmmm...uh huh....hmmm..... Nope. No sir! I don't like it!".
^_^
Paul L. Ming