You don't need to be a powergamer or have an interest in the best "build" to get frustrated with a character's abilities. And you don't need to be explicitly competing against the other players to realize your character isn't able to hold his or her own in a fight.
. . .
For example, I once played a 3e bard in the World's Largest Dungeon and soon learned to regret it. While there were some roleplay encounters they were few and far between so the majority of the bard's toolbox was left to get rusty while I spent battles saying, "I inspire courage... again." I might have been a useful member of the party, but the lack of combat options I had made for a pretty boring combat experience and I soon realized that this was not the right character for this game.
"Lack of combat options I had made for a pretty boring combat experience" may not be about power-gaming or one-upping other players, but it's not the complaint of someone who's focused on the story or on roleplaying the character.
I think my players ARE focused on story and roleplaying the character. I've seen them intentionaly make "suboptimal" character decisions or builds because it's who they want to play and the story they want to tell. I've got a player with a monk with an Int 18, because the player wanted a very smart, scholarly monk. Makes sense story wise, but it's crazy "build" wise.
And I don't think the variety of combat options is a problem. Most of us played AD&D, where combat for fighters was essentially "I roll a d20", "OK, roll for damage" -- there are way more options for any 3e character, so I don't think they'd be depressed by a 3e bard.
Actually, I think of bards as jack-of-all-trades characters, rather than just background musicians -- can rogue a little, wizard a little, heal a little -- so lack of choice doesn't seem like the problem to me. Not being as effective as a full-time character at any of these, so lack of EFFECTIVE choice, that I can understand.
The other issue for you is, World's Largest Dungeon really isn't a good campaign for someone who IS interested in their character's personality, social interactions, etc. From what I've played of it (never DM'd it), it's purely hack and slash, with no civilians to interact with, which is half the fun of a high Charisma character like a bard. So I get it that you might get bored, but I wouldn't think combat options were the problem -- just the lack of anything to do but combat.
I was playing a dwarven cleric -- optimized for survival underground, with high Con, high Dex, defensive spells, and infravision -- but I got bored because there didn't seem to be a point to it all. (And yes, I enjoy the defensive/supporting role of a 3e cleric.)
This could go the other way around, too. One of your players might have created a PC that's geared towards fighting only to find out that they're no good in the RP sessions of the campaign, and those come up more often than fighting, so the next session that player might want to retool their PC to be more effective at diplomacy.
My view is that not every character gets to be the star in every episode. Some of my adventures are geared to put one of the characters more in the spotlight, just like a TV series with an ensemble cast would do.
To use a Star Trek: The Next Generation analogy, if I'm doing a Worf episode, I don't want the guy who's playing Data to suddenly say, "Wait, now I want to be a great warrior too! I want to drop my feat in 'computer lore' and replace it with 'Klingon sword fighting'." That kills the campaign for people who do care about the story and the roleplaying.
But a good DM will build a good campaign, one that keeps it overall interesting for everybody, with a mix of challenges and situations.