When I first started playing D&D with the Red Box, it took me quite a while to wrap my brain around, because it's just so nonsensical. "I can do this, but I forget how every time I do it. Because... reasons.
Would be easier to accept if in place of using memory, wizards used speelbook pages? For example, after reading the only page containing a fireball spell and casting it, this specific page loses its magical power and cannot be used again. And, what about bullets in a revolver's chamber, ignoring order, loaded with three armor piercing, 2 incendiary and one regular type? My point is that the way the method is described resembles the influences that shaped early versions of the game and can be easily be replaced for new ones, while preserving the mechanic.
Speaking of which, what other mechanic can result in such close relationship between resource tracking and planning? Arcanists, 5ed wizard, etc, do not provide the same degree of challenge for the player as the vancian method does. A good wizard player is expected to know which spells, and what quantity of those, are most likely to be used in a given situation and learning this skill is part of the experience of playing wizards. And lets not forget the myriad of options like scrolls, wands, staffs and quick preparations, available to provide on the spot diversity.
Another advantage of preserving this method, as others mentioned, is that it allows the existence of spontaneous casting as an whole different mechanic. This time the compromise happens much earlier than for prep casters, as the choices must be made while leveling up your character, and the consequences last indefinitely. A new set of skills must be employed to make the right, or less wrong, choices this time. Again more opportunities for players to experience the game in a different way.
One could argue that players should be the ones making the choice of which method they want to employ for their characters, as this would represent the ultimate player driven characters making process. For this to be true, classes should not be defined by the way the cast spells or whatever, but for other attributes, specially narrative ones, and casting mechanics should be available in a different manner (feats, class features, etc).
To clarify, I am not arguing against the semi prep method, but in favor of preserving whatever diversity is present in the game at moment. For me there are other methods like cool down based classes, point based exclusively, etc, that should have been present in the core classes.