No it wouldn't, diablo3 did that and it is not as good as diablo2.
This only does one thing, everyone's champ will be the same, not good at all.

That certainly depends on the game and the tastes of the players. Some people just love to be punished - they want to hunt for that min-max perfection allowing them to beat an exceedingly difficult game. I personally don't find much joy in that. On the other hand build strategy shouldn't be meaningless either - otherwise I could just play any game without RPG mechanics. I guess in the end this is what difficulty levels are for.
Stuff like re-training, or "Potion of Clearance" always seem a bit like cheating to me - I can't reset my choices in real life either. I almost never use those options. "Role playing" to me means choice and consequences. Choices that seem valid, but are - by bad design - a total waste (Two Worlds' horse riding skill, anyone?) are of course a problem.

I guess one problem is that most RPGs don't like a Jack-of-all-Trades approach. For instance you need the most powerful weapons or spells to defeat later enemies, but dualled character won't have either. In party based games this is less of an issue, but people tend to spread out skills more in single character games because they simply want it all... smite the foe, cast the healing spell and pick the lock...

Another problem are games with unbalanced design, clearly favouring certain builds, punishing other, seemingly good builds.

You actually don't need permanent builds; you only limit how powerful the character can be at any point. Specifically:
* For online interaction, you really shouldn't have permanent builds at all. There are some situations where (long-term) growth systems are not suitable, and competitive gaming is one of them.
* Having a character able to be good at anything isn't the same as being good at everything. In FF5, for example, a character can do huge amounts of physical damage with Dual Wield + Rapid Fire + Spellblade (wielding the Chicken Knife), or you can have the same character be able to wipe out powerful enemies with Dualcast + Time (for Quick) + Summon (equip a Gold Hairpin because of MP costs), but you can't have a character able to do both at the same time. The first of those characters will be of no help if someone in the party dies (with this setup, there's no room for even the Item command, so that character can't even use Phoenix Downs). Also, note that the amount of ability points required for either setup is quite high (Doublecast alone requires 999 ABP), so getting either setup takes a long time unless you have access to the very end of the final dungeon (where fights finally give you 20+ ABP per fight).
* I think it may be better to have hard caps than soft caps here, or increase the cost of increasing the stat instead of having a soft cap.
That actually brings up another problem with skill point systems: They tend to reward hyper-focused builds and don't allow balanced characters, like Final Fantasy 1's Red Mage/Wizard, to be viable. (I note that D&D 3.x has this issue with its multi-class mechanics, particularly with multi-class spellcasters. If we look only at base classes, and ignore classes like Mystic Theurge (which was added later and is basically a patch for this issue), Making it more expensive to get later skills would solve the problem; decoupling skill points from level advancement (and providing an infinite source of them) would also help, capping one's skills could help, or even getting rid of skill points entirely and using a different system.

Final Fantasy 2 still has you build characters toward certain set-ups; having things like stats going down when another increases encourages that, as do the penalties to spellcasting caused by equipment (which should be made more visible to the player), having heavy armor slow the character down (though it turns out to be too much of an effect, and has the result of making heavy armor worse than useless), and the time it takes to raise weapon and spell levels. However, it does make it easier to raise skills that are lower, so old characters can learn new tricks, and it's at least reasonable to recover from a situation where your characters are so slow the game is frustrating rather than fun.

Interesting case:

In Final Fantasy 3 DS, Red Mages have that issue for a fair portion of the game, starting around when you reach the second world. However, it ends up not lasting forever:
* Red Mages have limited access to 5th level magic, which is strong enough for my RM to take over healing duties when my Devout needs to do something else during the final battle. (Not enough to be my main healer.)
* Red Mages have access to end-game equipment. Being able to use Excalibur, the Break Blade, and Crystal equipment allows them to actually fill a fighter role at the endgame (though before that there's a severe equipment drought for them). Perhaps the developers felt that, with the Sage class being available at this point, they wanted to differentiate Red Mages from them while having the classes balanced with each other, and I think they succeeded in this case.

(In original FF3, Red Mages were limited to 4th level magic and didn't get the likes of Excalibur, though they still got Crystal equipment for whatever reason.)