Perhaps you and your opponent were simply optimizing for different goals ? For example, it's possible that your goal was "defeat the opponent as quickly as possible", whereas his was "defeat the opponent while looking as good as possible (in order to derive maximum enjoyment from the task)" or "defeat the opponent whose challenge level falls within some optimal range, handicapping self if needed (in order to derive maximum enjoyment from the task)" . Your opponent may or may not have been aware of his true goals at the time.
My point is, it's kind of tricky to declare an action "worse than worthless" without having very detailed information about all of the actors involved.
If I am about to go and fence a bout, the color of the shirt that I wear under my jacket is of no concern to me-- but if I had spent significant time before the bout debating over what shirt to wear instead of training, it would become a damaging detail rather than a meaningless one.
Unfortunately, worrying about whether you should worry is also harmful for the same reasons. Luckily, that question should resolve itself more quickly, so it should be a net benefit.
However, in more difficult cases, worrying about whether your should worry is harder to resol...
Despite being at +13, this post has been somewhat controversial, with a positive vote ratio of only 73%-- I'd be interested in hearing what caused some people to downvote it.
My current feeling is that this comment should have been part of the original post-- I thought it was implicit, but evidently this was not the case. Therefore, I'm especially interested in hearing comments from downvoters who downvoted the post for reasons other than the above.
I've had many just such experiences in various sorts of gaming (World of Warcraft, D&D), attempting to teach less-experienced players how to play effectively. (I can elaborate if anyone wants.) I can attest that there's definitely a common attitude of "well, at most this is doing no good, and it's how I like to play".
In fact, one particular aspect of this is that people seem to place value on personalization — doing things their way. The problem is, if there exists some optimally-effective way of doing things, then most deviations are likely to make performance worse (quite often because, as the OP says, the modified/added action consumes resources or otherwise has an opportunity cost).
Here's an example from World of Warcraft:
In group content in WoW (i.e. teaming up with other players to kill big monsters — the high-end, maximally challenging game content), one of the key roles is the damage-dealer, or "DPS" (damage per second). One of the DPS classes is the hunter, a ranged attacker. The hunter's job is to deal as much damage to the enemies as fast as possible.
Like all DPS classes, hunters have a wide variety of damage-dealing abilities, with names like Aimed Shot, Arcane Shot, Serpent Sting, etc. Traditionally, damage-dealing classes use their abilities in complex, shifting sequences, called a "rotation", to maximize DPS. (The reasons for this are beyond the scope of this discussion.)
At one point, I was playing a hunter in high-end raid encounters, and consistently performing very well (doing significantly more damage than anyone else). I would often group with other hunters, who were not performing nearly as well. I often had conversations that went like this:
Other hunter: Hey, how are you doing that much damage?
Me: Oh, I just use Steady Shot over and over. Nothing else.
OH: Haha (they think I am joking)
Me: No, seriously. Look at the damage ...
I wonder what is the equivalent of the Steady Shot in real life that I keep ignoring...
Perhaps "exercise, go out to meet new people, and keep smiling"?
While D&D evolved from a strategy boardgame, it is still a role-playing game. As such, it includes storytelling elements, which, depending on your GM and the players' desires, may weigh far more heavily than monster-slaying.
Some GMs prefer to run their games as a straightforward dungeon crawl: encounter enemies, kill them, repeat. In this case, the optimal character would be the one who is maximally effective at slaying monsters, or supporting fellow party members who do so.
Other GMs introduce logical puzzles into the mix. In this case, while your character may be perfectly balanced for combat, it is still possible to lose due to failing to figure out the puzzle.
Still other GMs prefer to tell a story. In this case, the game is less about killing things, and more about pretending to be a person living in a magical fantasy world... A person who, on occasion, kills things. In this case, the optimal character is the one you enjoy playing. You could make a crossbow-Wizard (perhaps he flunked out of Wizard school, and spends his days fuming at the injustice, shooting other Wizards with crossbows to prove his superiority), a fat lazy Fighter (he used to be a Gladiator, but now he just sits around drinking ale all day, reminiscing about his trophies), an honest Rogue (the prison changed him, for the better), etc. The GM is not, of course, obligated to keep you alive; but at least your game will be interesting.
All of these styles of play are valid. Yes, your crossbow-Wizard won't be effective in combat -- but what if the game is not primarily about combat ?
Jiro has already responded on the central question (with a point that I had already made, but it bears repetition, and apparently keeps being missed when I say it, so my thanks to Jiro). The following is re: other issues mentioned in your comment.
Other GMs introduce logical puzzles into the mix. In this case, while your character may be perfectly balanced for combat, it is still possible to lose due to failing to figure out the puzzle.
Yes, but how does being ineffective in combat help you figure out the logic puzzle? Answer: it does not. Therefore: a c...
There are things that are worthless-- that provide no value. There are also things that are worse than worthless-- things that provide negative value. I have found that people sometimes confuse the latter for the former, which can carry potentially dire consequences.
One simple example of this is in fencing. I once fenced with an opponent who put a bit of an unnecessary twirl on his blade when recovering from each parry. After our bout, one of the spectators pointed out that there wasn't any point to the twirls and that my opponent would improve by simply not doing them anymore. My opponent claimed that, even if the twirls were unnecessary, at worst they were merely an aesthetic preference that was useless but not actually harmful.
However, the observer explained that any unnecessary movement is harmful in fencing, because it spends time and energy that could be put to better use-- even if that use is just recovering a split second faster! [1]
During our bout, I indeed scored at least one touch because my opponent's twirling recovery was slower than a less flashy standard movement. That touch could well be the difference between victory and defeat; in a real sword fight, it could be the difference between life and death.
This isn't, of course, to say that everything unnecessary is damaging. There are many things that we can simply be indifferent towards. If I am about to go and fence a bout, the color of the shirt that I wear under my jacket is of no concern to me-- but if I had spent significant time before the bout debating over what shirt to wear instead of training, it would become a damaging detail rather than a meaningless one.
In other words, the real damage is dealt when something is not only unnecessary, but consumes resources that could instead be used for productive tasks. We see this relatively easily when it comes to matters of money, but when it comes to wastes of time and effort, many fail to make the inductive leap.
[1] Miyamoto Musashi agrees: