Single-class characters should allow some flexibility for differentiation. 3ed had the perfect system at hand: Feats.
I wouldn't go so far as to call it perfect, but yeah, I'm a big big fan of feats.
In my personal experience, multiclassing is not really needed to create a character concept: if you have enough flexibility in feats/class features and also in skills and spells, YOU CAN create every character concept you can think about, eventually with the help of a make-up of flavor.
I disagree. Lets say a player wants to play a ninja like character (with or without oriental flavor) and in the players mind being a ninja means not just merely normal roguish ability but some sort of supernatural ability as well. Either I have to create a specific class that captures 'ninja' or I have to have a multiclassing system that lets you effectively marry a generic roguish class with a generic innately magical class to end up with a 'ki wielding master of stealth and evasion'. The big problem with going the 'ninja' route is that you tend to end up carrying too much flavor and fluff bagage into the class implementation, and then it becomes a poor fit for the elven pickpocket who supplments his mundane slight of hand with magical tricks. And if you end up adding another 'arcane trickster' class to cover that concept, you now not only have lots and lots of classes, but probably have mechanical diversity in that each class has slightly different mechanics for trying to accomplish a lot of the same things.
Suppose you have a character who is the martial champion of a god of song. Either you need a specific class for this deity and this role - 3e's Prestige Class - or you need a really good way to marry a generic paladin class with a generic bard class. And so forth.
I don't choose characters primarily based on the game role I intend to have in the party. I don't look at RPG's primarily from the focus of winning a minatures/exploration/tactical subgame. That subgame may be an important part of the game, but when designing a character I start with a concept and then look around to see what I can fit to it with the character construction toolkit that the system provides.
Third edition multiclassing is not perfect, in the sense that when it would be most useful its least available - character creation. But it is one of the most powerful character development systems ever implemented, and 4e suffers from its lack.
They want to be good fighters AND wizards at the same time. I am quite old-fashioned and I think a roleplay game is a game of roles, so pick one at a time.
Even granting you are old fashioned, 'a good fighter and a good wizard at the same time' is one of the most old fashioned roles and tropes in the book. It is the BD&D 'Elf' class. And the very fact that the race was a class is I think a fairly strong illustration for what I explained above for why multi-classing just works better in the long run. Talk about carrying too much specific fluff into a class implementation.
Of course 5e should cater to everyone, so multiclassing will certainly be included. Also, after all it's better to have a single decent multiclassing rule than dozens of additional classes which essentially offer nothing new but a mix of the core classes. Both of these for me are inferior design choices than having a small bunch of core classes with good flexibility.
Ok, nm then. I guess we do agree after all.
I've seen it all the time in 3ed players writing up multiclass PCs (except beginners and spellcasters) and then complain that the game didn't offer good reasons to stay single class. Ban multiclassing from the PHB and you have your reason
This is I think do to some poor specific implementation details and choices rather than a general problem with multiclassing.