Actually, there's PLENTY of reason to beleive the barbarian can't do any of these things. Barbarians by archetype are savage brutes, uncouth outsiders, dirty and smelly and a half-step above a beast.
Not sure where you get this from. If anything, it seems like you have a "bias" against barbarians. Savage does not mean inept.
The archetypical Conan isn't some kind of incompetent fool who is only good at making attacks, nor is the 3e barbarian, which has only 2 skill points less than the bard (they were actually equal in 3.0) and several noncombat abilities. Can't speak to the earlier D&D versions.
Well, why would the bard ever risk their own death when there are so many people willing to leap to the bard's defense and obey their every command?
This sort of reminds be of Batman Begins, in which the Scarecrow creates a criminal enterprise and does a variety of things and has tons of henchman and barriers around him, only to melt in Batman's hands and unceremoniously get knocked out. (And indeed, the film was praised for not trying to make the Scarecrow into some kind of martial artist and throw in a needless fistfight).
Social ability is great, but it's not always a substitute for being able to get stuff done yourself. There are a variety of D&D contexts in which even a bard surrounded by allies (for some reason) can still be subjected to attack and will still die fast. Bards dying fast is something of a trope in D&D, as The Gamers movie noted.
I don't think "I'm more useful than my peers in certain situations" is much of an unreasonable expectation. I do think that D&D's design has made whether or not a bard player can hit that point pretty scatter-shot.
Of course not. I'm not anti-bard, just anti-bard as an equally viable adventurer.
After all when I rewrote the bard, I greatly increased its abilities. I took the daily limits off of its special abilities, gave it unrestricted bonus feats, added in some more new stuff. What I didn't try to do was make it specifically to compete with the other classes. I simply made it the best bard it could be, because I had a player who expressed interest in playing one for my campaign involving royal families and court intrigue. I expect if it ever sees use it will turn out well.
I also expect that if another player plays the barbarian I wrote, the barbarian will have the ability to kick the bard's ass.