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:
The primary thing when you take a sword in your hands is your intention to cut the enemy, whatever the means. Whenever you parry, hit, spring, strike or touch the enemy's cutting sword, you must cut the enemy in the same movement. It is essential to attain this. If you think only of hitting, springing, striking or touching the enemy, you will not be able actually to cut him. More than anything, you must be thinking of carrying your movement through to cutting him. You must thoroughly research this.
Social interaction is just one example; I picked it because it is the most common. That said, I would argue that making a character with zero social skills (in order to put those points into more combat) would restrict you to a fairly narrow subset of roleplaying opportunities.
The key to my point, though, is something you said: your character sheet should, ideally, represent your character. This is less apparent in D&D, where most of the mechanics are combat-oriented; and much more apparent in other games, e.g. the old White Wolf system where you have explicit ratings in things like "Bureaucracy", "Law", "Resources", "Contacts", "Allies", and even "Performance", IIRC -- alongside the more combat-worthy stats such as "Firearms" or "Dodge".
However, even in D&D, there are ways to represent your character's non-combat abilities which, unfortunately, compete for points with the combat ones. Here are some examples:
Is your character a self-appointed prophet ? Well, then you should probably take "Spell Focus: Divination", as opposed to something more battle-worthy. Is your character a skilled craftsman ? Then you should take a bunch of item creation Feats instead of going deeper into the "Power Attack" tree. Were his parents abducted by crab-people ? Then the crab-people are probably your racial enemy, despite being incredibly rare.
Are any of these tradeoffs crippling ? No, but they do add up, and while you are now better at crafting arms and armor and making money doing so, you are no longer as good at cleaving things or (e.g.) swimming as you could've been.
Of course, you could reply with something like, "only a fool would make crab-people a part of his backstory; just make your parents be abducted by humanoids, instead". If you do, see my objection #3 in the previous comment.
I disagree. (As a side note, it's actually not very easy to put skill points, specifically, into "more combat", with a couple of exceptions.)
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