It seems there are two reasons a player would want to dual class: 1) to intentionally obtain the powers of both classes-- become the sword wielding mage, for example, or 2) because they became dissatisfied with the class they started with.
I'm not really interested in 1. You can do a ton to personalize your characters before needing to slide into another archetype's realm. Want to be a badass fighting mage? Research a lesser version of a spell like 1e's Tenser's Transformation, get a magic staff or darts, learn the protective spells that will enable you to enter combat. Want to be a magic wielding fighter? Find some potions, protection scrolls, some magic rings and learn how to use them.
1 doesn't really make sense to me either in that you are gaining your experience serially, so if you want the fighting mage you have to plan several levels of one class and then a switch. See here for my personal experience with that.
2 I'm quite sympathetic about. My players starting out usually have no clue what the classes can do. Fighters are a straightforward safe bet. If, after three levels of fighter they realize they are missing out on a lot of cool stuff available to magic-users, and wish they had tried that class many months ago, I am quite tempted to let them switch.
The interesting thing is that the rules seem to assume situation 1. By raising the bar for dual classing to a 16 required in the second classe's main attribute, it seems intended to limit the occurrence of these potent combined power characters. And yet, this rule makes 1 much more likely to happen then 2. Unless you are doing a newer school style of stat rolling, 16's will be rare. My fighters wishing to switch are out of luck. The more experienced player who knows the rules will see the 16 when he rolls it and know he can dual class this character.
Another thought is, for situation 2, why not just give them a new character of the class they desire? I see two sticking points. One, if they roll up stats the way we do there is no guarantee they will get the numbers needed for that class, and two, they will lose all the experience they gained unless you jump the new character in level. I hate jumping people up in levels. Yes I know Gygax did it, yes I know there are con events that play high level pregens. To me that is like setting up a Jenga game with half its blocks already missing. D&D is about progression, about the hard-scrabble gaining of power, no one is jumping to third level in my campaign (will I change my mind on this as I become more enlightened, maybe, but it's how I feel now).
Maybe a compromise for me is my player could switch classes and keep their hitpoints and save but nothing else from the original class and ignore the stat requirement. This would mean all the experience they earned was not wasted, those hitpoints will help buff their feeble apprenticeship in the new class. That doesn't solve the problem of having appropriately high stats for the new class, but heck, maybe my world needs some dumb magic-users and puny fighters.