This is actually completely incorrect.
The person who is okay at A, B, and C is going to be solidly viable in any situation. He's the universal party backup. When the guy who is great at B, fails at B because the dice gods say so, then the guys who are okay at B are great for backup.
He will always be there to save the party's bacon when a roll goes south. He will always be able to contribute. That is NOT less than viable.
Also, have you EVER played an AP with 4 people who are all "okay" at just about everything? I have. They steam roll the AP so hard it isn't even funny. Nothing you can throw in their path even starts to slow them down.
Now, run an AP with 4 optimized PCs and watch the look of terror that happens when something goes terribly wrong. When the Ogre in Ft. Rannik lands a critical hit on the party cleric and drops him in one shot. Watch as the party scrambles, in complete back peddle mode, begging to retreat to get to somewhere they can raise dead.
Watch the look of horror on a GM's face when, for the party to proceed, someone has to make a roll and the guy who was the "perception guy" just rolled a 1. Who suddenly has to pull something completely out of his rear so the game can continue.
The Optimized party is better... When everything goes right. I admit, it...
This is just false.
Yes having backups for things is good. In fact my hypothetical specialized party had backups, skill guy with secondary combat ability, combat guy with secondary skill ability, buff/healer/support with secondary combat ability, primary caster with secondary buffing and nuking ability. As far as when a AP of average characters steamrolls lets be honest AP's are laughably easy and the most common reason you see the optimized party get killed is because the DM overreacts to him not "winning" in combat and upleveling the encounters without taking into account the party dynamic.
Also your example of the paladin makes no sense. Look at my subsections for specialization 3 out of the 4 things you list as reasons a Paladin is good are Combat abilities and 1 of them is secondary healing this is an example of specializing. The real reason the paladin is better than a fighter is two fold, 1) He's a better combatant than the fighter. The reason for this is that he's more resilient overall. Has better saves, some healing, and better burst damage on smites. and 2) Because the paladin can have secondary abilities in addition to his primary ones with more skill points and spells to fall back on while Fighters generally can't do this with the same amount of investment.
This does not mean that the Paladin is not specialized, in fact he should also specialize. If he's an archer he should pick up archery feats, if he's going into melee he should pick those feats, yeah keep a bow on hand even if you're a greatsword weilder and vice versa because any damage is better than no damage if you have to use it but trying to play a switch hitter mystic theurge or bard for all the characters in a party is not good.