There is a notion that I think is pretty close to the truth, that it takes ten years to master any complex skill. Ten years.
I also think that people underestimate how skilled and talented first-level characters are in classic D&D. "They can be killed with just one swing of a sword" is a common lament. Somehow that's supposed to mean that a first-level fighter, for instance, is not that exceptional. (Well, yes. Everyone in the real world can be killed with just one swing of a sword, too. This guy has a chance of surviving two or more.)
On a related note, I've heard people joke about how 1st edition AD&D had laughable names for the class levels. As evidence, they point to how a first-level fighter is called a "Veteran." People who think that that's a misprint or a gross error just aren't getting it, I think: even first-level characters are meant to be exceptional people, in other words, people who have mastered, or are on the verge of mastering, their professions. People who already have experience.
In our daily lives, most of us just don't have that kind of single-minded discipline, or don't find ourselves in positions that force us to undergo that kind of strenuous training, so it's hard for us to imagine the lives of people who do. It may even be a sign of mental imbalance. Look at Bobby Fischer.
Think about how much background work is necessary to have even a first-level character: a fighter might have a training sword placed in his hands at the age of seven, learn archery by holding a drawn bow still for a half hour before firing his first arrow, or be knocked down by a blunted blade ten thousand times so he learns how to take a blow, and then later avoid it.
Think of the esoteric knowledge that a magic-user needs to learn: knowledge of the planes, and the nth-dimensional math required to understand their relationships, the understanding of alchemical and herbal substances, the secret names of things, and a preternatural ability to remain calm while channeling forces from other dimensions through their body.
Try to imagine the iron discipline and daily punishment a monk needs to put his body and mind through before gaining first level. Meditating on sutras while ice-cold waterfalls crash around them, pounding their hands into the sides of trees until their knuckles are toughened leather, and balancing on stumps while dodging spears and sword slashes from their peers. None of these are things to be undertaken lightly.
In that light, I don't find 1st editions restrictions on multi-classing that hard to accept or understand. If you do make that switch, you are saying that you've made a massive effort to re-eductate your mind and body (something that Michael Jordan wasn't able to do), and not only learn new things, but learn how to be a different being. It may happen, but it happens at a cost. It explains why non-human characters like elves can multi-class; they live so long, ten years isn't the same obstacle for them as it is for us. And less long-lived characters can explain it by saying that the skills needed just to survive in their environments or societies means that some degree of multiple class skills are drilled into their heads from day one.
That's why I find it hard to swallow when, in Pathfinder for instance, someone with three levels as a cleric suddenly decides "I'm going to take a level in monk." I hear that as, "I'm going to learn what it takes any other person ten years to begin to understand, and learn it overnight."
Unless a radioactive monk bites you, I just don't see it happening.