I believe archetypes are better because they are simpler to understand and work with. It is easy for people to say "Wizard, that's the guy who casts fireballs and lightning bolts at people" or "Rogue, that's the sneaky guy with the daggers who stabs people in the back". These archetypes are intuitive, they are the kind of things even non-gamers thinks of when these words come up.
Isn't this an argument to remove customizing altogether and hand out pregens? even the most slightly option to customize opens room for breaking out of these "platonic archetypes" you mention. (Which aren't that useful considering the huge diversity of characters in fiction. Going by your wizard definition, Merlin has no place in the game -he never went out blasting the enemies of Camelot with fireballs and lightning bolts- not even good ol' Gandalf is good enough for the game -how he dare wield a sword?- )
Not to mention the other player's feelings when these characters are doing well: "I'll heal you! I'm a cleric and I specialized in healing!" "No thanks, I have a class feature that allows me to heal myself. Did I mention I also have the best AC in the group, the most hitpoints and do the most damage? It's cute that you think I need your help. Since all you can do is heal and I don't need that, why don't you sit over there and I'll let you bring me ale when I'm done killing the enemies."
You know what hurts a focused healer's feeling more than "no thanks I can do it myself" ? Being told "no thanks, the system will fully heal me overnight without having to spend a single resource". Also powergamed Clerics could do this on 3.5 and without needing a single multiclass. So, you see, multiclassing has nothing to do with brokeness on itslef
I'd imagine that given a Str 3 fighter could barely lift a sword that they'd be really bad at fighting. Realistically, swinging a sword around all day, practicing with heavy weapons and armor and being physically fit enough to strike blows through armor and do some of the maneuvers required to fight with all the weapons fighters are trained in, there would be a minimum strength required. It would be above average.
Then again, I think that the point of the system is that your character IS their primary class, they are just dabbling in other classes. I generally think of someone who starts as a level 1 Wizard, for instance, to be someone who started training at a young age, practiced for years to get everything right and is now a full fledged Wizard. A Fighter who multiclasses into Wizard is instead the guy who spent his entire life training with weapons and armors and practices martial maneuvers. He then picks up a spell book one day and says "I'm going to learn magic. I have 2 weeks, what can you teach me?" Only people who are exceptionally intelligent can learn magic in such a short period of time. They have to be able to read and understand advanced topics quickly. So they need to be REALLY naturally talented.
As for the Fighter who is str 3 and Dex 16. They might be a great fighter according to the rules, but I hate when people refer to the rules for everything. The rules MEAN something in the game world. Even though the character is mechanically super awesome, the character in question is a little absurd. Mechanically a 3 str doesn't hurt this character at all. That's because the rules are attempting to be abstract and easy to learn. In the game, the character has a max load of 30 lbs and shouldn't be able to effectively wield a sword at all. I wouldn't ever make this character. I'd also look down at someone who tried it for powergaming.
You know, there is a reason light weapons exist, even a machete is light enough to be carried comfortably by a young child with a single hand -not that small kids should handle bladed things, but they are capable of that as long as the weapon isn't taller than them-. And wanting to play a very weak fighter can be interesting on itself, it has nothing to do with powergaming but wanting a certain character. (and if that is the case, why my Str 8 ranger can be a ranger, but never start to seriously train and become a more focussed fighter?)
Besides, mark my words. Dipping and dabbling aren't the only reasons to multiclassing. As I've already stated over and over there are six basic reasons to multiclass
Rounding up - Get a perk for your PC
Dabbling - Get some extra ability to rely on
Mixing archetypes - the classical fighter/mage goes here, though it doesn't have to be 50-50
Organic Growth - Reflect changes on your characters life by changing class in response to the campaign events
Make-your-own-class - Express an archetype that hasn't been expressed in-game. Fringe things such as "Elven righteous nimble slayer of evil tiefling mages"
Powergaming - Nuff said. Though this can map to any of the former.
Even the last one can be legitimate with the right group.
I don't have any examples from D&D Next. Though if I did they'd be pointless anyways, since I don't have access to at least 2 of the classes and a number of options that will be in the final game and many of the issues are likely already fixed.
But there were MANY examples of this back in 3.5e. Almost all of them were caused by multiclassing like crazy. I remember at least one character I made who wore heavy armor, had a crap ton of hitpoints, had a +17 BAB at level 20 and could cast 9th level spells with no spell failure chance while wearing his armor. He had a feat that let him channel spells into his weapon to do an extra +9 to hit and +9d4 damage while making his attacks touch attacks. It was extremely powerful. It required me to have 5 different classes to get all the class features, however.
Don't get me wrong, I'd rather see a different system for gating in possible over-multiclassers. But this one works well enough to at least prevent the worst of the issues.
Cof, Cof, CodZilla...
More seriously, how many of those five classes were Base classes as opposed to Prestige Classes? As far as I know no base classes ever stacked spellcasting.