I have to agree that this would not work well with multiclassing. Or at least multiclassing as it currently exists.
Pre 3.x multiclassing was parallel - all your classes were picked at creation and you divided your xp between them. You started out in level 1 of all your classes, but each class only gained a fraction of your XP total and progressed accordingly so differing XP tracks were not an issue.
Post 3.x multiclassing is serial - you start out with one class and then at any time when you level you can take a level in another class. This necessitated going to a unified XP track instead of individual tracks for each class. Prestige classes only add to this.
Theoretically you could track all XP separately by class, with each class added by multiclassing adding a new track starting at 0. However all you are adding is a lot more bookkeeping. Additionally there is the issue of "how much XP to add a new class?" which if you go with "enough to level in an existing class" gets progressively higher the more levels you have. This would encourage taking 1 level in each class as early as possible. Your character sheet would end up looking like a character ledger.
Then there is balance issues with CR, average party level, and character level that would have to be considered.
Not quiet as simple a fix for martial/caster disparity as it would appear.
Remember changing one rule impacts every other rule that interacts with it.