You're completely missing the point. Thoofus is the counterpoint to the barbarian. He has the minimum Charisma needed to cast his spells, no ranks in and Charisma-based skills other than Perform, and no spells that assist interactions. Your example was of a bard who was maxed for interaction and a barbarian who was minned (?) for interaction. This is the opposite.
Bards get L6 spells, so he needs a 16 CHA eventually. I'm curious what Thoofus is focused on, but that's beside the point. Sure, if the Barbarian is max'ed out for interaction, he would be better at interaction than a character who put no resources into interaction. Of course, if that 16 CHA, 14 WIS Barbarian is a half orc, and is using the 28 point buy mechanism (rather than, say, "roll 4d6, drop the lowest, arrange as you like, roll as long as you like and keep the character whose lowest stat is a 14"), he has spent 6 points on WIS and 16 on CHA. That leaves 6 points to have a 12 STR (10+2), 10 CON, 10 DEX and 6 (8-2) INT. He spends half his 2 skill points per level to get Diplomacy ranks equal to half his level, so by L7 he has +8 Diplomacy (+3 from CHA, 5 ranks).
If Thoofus spends all his base 6 skill points next level on Diplomacy, and has that 16 CHA for his eventual L6 spells, he passes the Barbarian, achieving a +9. If he maximizes his Diplomacy ranks at L7, and has a 16 CHA, he has +13. Just as Bard is not the best chassis for a melee amage machine, Half Orc Barbarian isn't optimal for diplomacy. But if that's how they built their characters, then:
(a) The Barbarian will do better at diplomacy than the Bard;
(b) The DM should discuss the objectives of the players - if he runs a game with CR 7 opponents, I think that Barbarian is in trouble, and if the Diplomacy DC's are set in the 20 - 25 range (where a reasonably optimised Diplomat would have a 40% to 2/3 shot at success with no work to enhance their odds, and a very good chance if they can get some modifiers by, say, evidence that discredits the opposition, learning about the Duke's biases to tailor their arguments accordingly and securing support from other advisors the Duke trusts to get a couple of valuable Aid Another's going), their social challenges will be pretty hit and miss as well. [Example: DC 25, but you can get +2 from evidence the other faction is funding a scandal sheet that targets the Duke, +2 more by incorporating how good this will look in the Duke's biography, presently being written, and 2 trusted advisors' support can be attained by various side quests for another +4, that +13 becomes +21, so 85% likely, while that +8 becomes +16, 60% likely - more than double the chance of failure).
Basically, the original example you gave was cherry-picked to make the barbarian look bad, so I turned it around.
I think low CHA half orc barbarians with social skills limited to Intimidation are a lot more common than 16 CHA ones who max out Diplomacy, but YMMV, I suppose. Unquesionably,my example featured a character focusing resources on interaction skills, and a second dumping them. I'd suggest a Barbarian focuses a lot on melee combat damage, and a Bard essentially dumps that, at least as an area of primary focus.
They were also stated. The first one is that trying to create that kind of equality usually fails outright. The second is that the efforts to do so often undermine the character concept being altered to be more "equal". A third would be that it discriminates against players or DMs who want unequal characters for any number of reasons.
To the first, we can get closer without perfect success, or we can give up. I prefer the former. To the second, this depends on whether one views one aspect of the character concept to be "capable player character avbenturer". I do - anything not fitting that mold should be an NPC class, IMO. To the third, nothing precludes taking levels in those NPC classes, providing more character resources to some players/characters, greater use of random character determination and/or having characters of unequal levels, to meet the desire of anyone wanting unequal characters for any number of reasons.
Clearly, however, my bias (again, not a negative term, in my view) is to default to maximum equality of character choices, and leave unequal characters as a variation if the players/GM wishes to do so, rather than have character disparity be wide by default, with options to better level the playing field. Increasing the disparity betweem character power seems a lot easier than reducing it.
You kind of can, actually. Sometimes it follows from mechanics. Sometimes I make certain decisions about what conflicts they'll face (sometimes with regards to the player before a character is even made). Sure, things can change during play, sometimes a lot, but that doesn't mean that everyone sits down at the table with the conceit that all their characters are exactly equal. They're not naive.
If we already know how the campaign will turn out, why play it? Why don't you just write up the story you've already determine will play out and email it to us? Clearly (or at least I hope), your expectations are not as complete as that, but I don't think anyone shows up at the gaming table with a character they expect, even hope, will be killed off before he reaches second level.
In the pantheon of things an rpg needs to be, "feels real" is well above "all characters must be equal", along with its variants "makes sense" and "doesn't break immersion". So is "players can make the character they want", "DMs can create the game they want", "game plays fast and easy". If the choice is between letting one player choose a character type that's better than another character type that may or may not be selected by someone else, and homogenizing those characters, the choice is easy. It's only after all the roleplaying part and the game part already do everything that they're supposed to that you can start worrying about this kind of stuff.
Feels real? Yup, nothing like fire breathing dragons, spell-blasting wizards and tauric halfling blink dogs to keep it real! That last one isn't helping me a lot in the "makes sense" department either. I suppose it would "make sense" if everyone trained in magic and soldiers were replaced with golems and such, but I like having martial classes too. Not breaking immersion, I will agree is a big one, but I don't think "the PC's don't include guys who can't pull their weight" is a dealbreaker there (and again, I refer back to tauric halfling blink dogs...).
"players can make the character they want" - like a Bard suitable to adventure? "DMs can create the game they want" - what if this conflicts with the previous one? I don't see character choices being more or less equal by default having a negative impact on either of these - maybe the first if the desire is "a more powerful character than the other players", but what happens when two or more players want that, or another wants "more or less equal powered characters"?
"game plays fast and easy" is pretty subjective. Not sure how many RPG gamers wouldn't suggest that ship has already sailed - wy don't we go back to the Blue Book rather than a three volume starter set of rules? Heads the characters succeed and become leaders of their own kingdom, tails they die in a ditch is very fast and easy, but hardly satisfying. To the extent this is achievable (and it's achievable with way more depth than my Coin Toss Campaign example), I don't see default equality or inequality of choices hitting that hard. If anything, the quest for an optimized character seems a lot slower and more difficult than a system where any concept you choose will be fairly balanced with the other choices.
Of course, I guess if things are so unbalanced that one choice is clearly superior, so everyone plays one of those, that's also quick and easy character creation - we can just copy that sheet in bulk in case one of the clones dies. More realistically, if we can eliminate some choices, that simplifies matters. Let's consolidate back to Fighting Man, Magic-User and Cleric, maybe? All humans, no skills, no feats, all weapons do 1d6?
It's a balancing act, to be sure, and every one of these areas falls somewhere within a range of results - with many different views as to the ideal balance between them, and what points in the range are, in fact, acceptable, much less optimal.