I know I saw groups where no player would ever bother playing a "switch-class" Human, but there where also others where it was pretty common, and generally considered superior to multi-classing as a demi-human. The groups I primarily played with mostly had individual human characters as single-classes specialists and demi-humans as multiclasses (except for Dwarven & Half-Orc Fighters), but overall I'd still rate humans as generalists, simply because they had access to any class!
Except, once a human says "I'm going to be a fighter", his options are limited. Unless he has super high stats, he may have only one other class to dual-class into, if that. So, he's not really much of a generalist. At least, that's how I'm seeing it.
As an example, let's say we have a human with stats of Str 17, Dex 17, Con 13, Int 13, Wis 13, Cha 13. Those are pretty good stats. And let's compare him to an elf of the same level, with the same stats.
At the start of the game, the human has two big options - Fighter, or Thief. He decides to be a thief. After a few levels, he can dual-class into, um, Fighter.
The Elf, on the other hand, has MANY more options open available to him at start. He can be a fighter/mage/thief, a fighter/cleric/mage, a fighter/thief, a fighter/mage, and so on, and so forth.
So, yeah, the human has all those options open to him... until he makes a choice at character creation, and then he's set. And he can only pick one class (and possibly branch out into most likely one more class later on). In comparison, most other races have wider options.
So, I say humans are specialists, in 1e/2e.