Arial Black
Adventurer
I've actually started a kickstarter to raise funds so I can fly over to Arial Black's location and do just that! 20$ gets you the video, 50$ a signed USB key!![]()
Bring your own snacks.

As for what you want out of this thread, once the players know how to play (so there is no further need for 'training wheels') they will want to try new character ideas. You can limit them to the 12 in the book, but multi-classing raises that number by literally thousands, all by looking at the class descriptions of those very same 12 classes!
I wanted a secret agent type spy, so I made an assassin rogue/shadow monk. I wanted a pirate captain who wants the world to think he is vicious and ruthless while secretly working for good, yet while he thinks he serves Odin he actually gains power from a fiend without even realising that his 'raven' familiar sent from Odin is actually a polymorphed imp sent from the fiend to slowly corrupt him over time, so I made him a vengeance paladin/fiendish chainlock.
I also wanted a swashbuckler, and I made a single class battlemaster. He's 7th level now, and hard as nails.
When I chose to multiclass it was to realise the character I had in my mind. The process of multiclassing did not take away from the backstory or role-playing at all, and it is a fallacy to imagine that you must sacrifice one for the other.
When TSR tried to make Elric of Melnibone for 1E in Deities & Demigods they had to make him so multiclassed that he broke the 1E multiclass rules, something like Ftr 13/Assassin 10/Wiz 17, IIRC. It would not have been possible to realise that character as single class. Why deny your players that opportunity?
Is it more complex? Not in play! In actual play, a multiclass character has X levels worth of special abilities just like any single class PC of the same level. It may be more complex to research when levelling but your player does that, and he puts that effort in because he wants to; no skin off your nose.
If I joined a new game, I wouldn't take my bat and ball home if the guy next to me had a single class OR a multiclass PC; as long as we were the same level I'd have nothing to complain about. I would be astonished if someone left a game because someone else's PC was multiclassed!
For example, my pirate captain (who's brilliant to play BTW!) can do a lot of cool stuff as a pal 2/war 3, but he doesn't get two attacks per round like the bar 5 and can't cast 3rd level spells like the clr 5, so what I gain on the swings I lose on the roundabouts. I'm totally happy about it. It would be patronising to believe that I might not be able to cope with my own choices.