To be honest, I like this version of multi-classing. Sure, it's somewhat "gamey," but it's just a neat idea of a character shifting his or her focus every so often to the skill set she needs the most, and it points to a certain alien mindset to the demihuman abilities that isn't shared by humans. But only elves get the option.
Later, dwarves and hobbits get the option to simultaneously advance as thieves and fighting-men, but elves then gain that option as well as the option to advance simultaneously in all three classes, or they can stick to their "every other session" method.
In thinking about this, I came across a passage in Supplement I: Greyhawk (page 5), which caught my interest. It reads:
Among the dwarves themselves, but never as a player, there are clerical types. Dwarf clerics are found as high as 7th level (Lama), and they can cure and resurrect their own. These clerics are also fighters.
First things first: Why not as player characters? Heck, in OD&D Vol. 1 (page 8) it reads, "There is no reason that players cannot be allowed to play as virtually anything, provided they begin relatively weak and work up to the top..." And we even have a level limit (7) in place.
So it strikes me, all that being a given, that dwarves could be run just like elves, save that instead of switching between fighting-man and magic-user, they would switch off between fighting-man and cleric.
What, then, about hobbits? Well, hobbits have only two options: fighting man and thief. But there's no reason why we can't let them exercise those two options just as elves (and now dwarves) do.
So then we have elves who can switch off between MU and FM, dwarves who can switch off between C and FM, and hobbits who can switch off between T and FM. And suddenly, we have parity amongst the races. Not only that, it makes for some very cool archetypes in play and the hobbits, at least, seem to better fit the mold of Tolkien hobbits that way.
Now some will say, "why do you need parity amongst the races?" To that I answer, "you're right--you don't. The game works just fine without it." It's just been a pet peeve of mine, a little niggling thing at the back of my head. Why were elves portrayed that way and not the other races? Probably because they were trying to emulate Tolkien-esque elves, but I'd argue that the natural stealth and nimbleness of hobbits demands that once the thief class is introduced in Supplement I that hobbits be handled the same way between Fighter and Thief.
With dwarves, I dunno. I just think it's a really cool image, the fighter/cleric who is so connected to the earth in which he lives that he can call upon natural clerical-type magic and powers. It kind of, to my mind, makes dwarves more primal. Especially if their gods are earth and rock spirits instead of actual deities.
I may adopt this concept in future D&D games I run.