A problem I have with this is one of bookkeeping. What if one has five or six classes? -- and there is nothing under the rules to say you should not. Sucks to have to track five or six xp totals.
No system in this world exists that can't be overtaxed by the human mind creating more than enough work for itself. Trying to track five or six classes is no less bookkeeping under 3E rules, where you deal with e.g. one list of class skills for each class.
But a larger problem I have is that this is inelegant.
See, the elegance of 3E D&D is the central idea that the quantum unit of character building is the level. By piling level upon level, you can create a wide array of different characters. To make this work, a fundamental idea is that All Levels Are Equal. A single common xp total, a single common base attack bonus, a single common set of saving throws, and -- in one of my proposals -- a single common caster level unite these building block levels, and each level makes a contribution to the total.
Your suggestion reminds me of first edition. A magic-user 5 / cleric 5 would use whatever was better of the two class's saves and attacks. I think the 3E way is better.
That's what I thought, too, for some years. But you only need to take a little deeper look to see that this cute idea of all levels being equal simply doesn't work in 3E, and never really did, and more so if you are have a caster class in the mix. A fighter/wizard 5/5 simply isn't comparable to a 10th level single class character in power, and hence will get sacked by monsters of adequate CRs even easier.
And yes, astute observation about the source of the inspiration for the idea, although I said something about 2nd Edition in my post, since I never played AD&D 1E.