multiclassing in 3E was a double edged sword. On the one hand, when they first released the new rules, I loved how they simplified the multiclass system. That part of D&D had always been frustrating IMO and this really reduced some of the quirkiness. It really did make a difference for me. But as you point out, the class dipping and the unpredictability of some of the combos produced....unexpected results. This could work if you embraced, it could also work if you worked hard to curtail it. For me, really emphasizing the in game time investment made a huge difference. You didn't just take a level in x when you felt like it, you had to put in the training and often seek out people who could induct you (in the case of classes where there was that slrt of requirement). I think 4e responded to a problem many people genuinely had with the game. I dont fault them for tackling it and the way they went about it was more like classic D&D I think. But I would really like to see an effort made to preserve the flexibility and simplicity of the 3e multiclass system while eliminating mnag of its excesses.
I feel very similarly, although as a DM I came to despise 3.x multiclassing more than most players seem to. I prefer to run games with mostly non-monstrous NPCs, and all the 3.x multiclassing warts got in my way virtually every session. Its one of the things I dread most about what they've said regarding 5e.
The last time I really mused on "fixing" 3e's multiclassing, I was thinking that the system really should have differentiated between evolving into a prestige class and picking up another base class. Also, I think it could learn from the earlier editions, since not all 3e levels are the same. I think CnC's methods can help point the way here as it uses simultaneous multiclassing.
I was thinking something like this: (very sketchy, HP would have to be worked out, and skills for 3e, but Backgrounds make that easier in 5e

)
Multi-classing from first level: You can take more than one class at once and be, say a Ranger-Wizard. If you do, you start at -2 levels for the first additional class, -3 if you triple class. Whenever you gain a level, you advance one level in each class' abilities.
We'd need to extend class tables down to level -3, but those tables could be in the multiclassing section.
Take a class-and-a-half: You have a primary class, and a secondary class. You start at level 0 (an effective -1 penalty). Whenever you gain a level, you gain a level's worth of abilities in your primary class. Your effective level in your secondary class is one half of that rounded up.
Splash a class: Add some multiclassing feats a la 4e. (5e has already done this, I think.)
Prestige classes: If you meet the requirements for a prestige class, you may start taking levels in that class instead of your original class.
Prestige classes would be designed to stack better, possibly even specifying the base class(es) that would lead into them.
Non-prestige multiclassing after character creation:Example; you're a Ranger 5, and you've had a change of heart and want to be a Wizard now? Okay, follow these steps.
1) Take the relevant "Splash" feat. (If you haven't already) In 5e, this step might be irrelevant, as the "splash" feats seem pretty good, even for the associated class IIRC.
2) When you would next gain a level, instead gain the benefits of a class-and-a-half with your new class as the secondary class. If you do, you do not gain a level in your original class. Our example would then be a Rgr 5/Wiz 2. You may then choose to advance as a class-and-a-half character with your original class as primary. If you wish to further abandon your original class, proceed to step 3. (Probably, you can re-train that "Splash" feat..or not, depending)
3) When you would next gain a level, instead gain the benefits of full multiclassing. If you do, do not gain a level in your original class. Our example would then be Ranger 5/Wizard 5. If that is all you desire, continue advancing from that point as a normal multi-class character. If you are abandoning your original class further, continue to step 4.
4) The next time you would level up, gain 2 levels of ability in your new class, and drop your level of ability in your first class to one half of that rounded down (if necessary). Our example character would become Wiz 7/Rgr 3. You may then proceed as a class-and-half character with your new class as the primary class. If you wish to further abandon your original class proceed to step 5.
5) The next time you would level up, gain 2 levels of ability in your new class. If you do, you loose all ability in your old class. Our example character would then be Wiz 9.
I figure by the time the math for this starts to get wonky, you're probably also looking more for prestige multi-classing, rather than switching classes.