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.
If we're being strict, then you're actually arguing against the converse of what I said — whether being effective in combat negatively impacts your roleplaying or interestingness. Which I also don't think it does, but it's a distinct point.
My actual point, in any case, is that there are many ways to roleplay. You can roleplay well and be interesting with a Charisma of 7 and zero ranks in social skills, and then again you can roleplay well and be interesting with a Charisma of 18 and maximum ranks in social skills. You'd be roleplaying different things in those two cases, presumably; but, you can have an effectively-built character in both of those cases as well. (The former might be a wizard, or a fighter, or a rogue, or something else; the latter might be a sorcerer, or a paladin, or a different kind of rogue etc. etc.)
It is an accepted truism among all the veteran D&D players I know, and have spoken to in various online gaming communities, that a good roleplayer can create an interesting character concept, and roleplay it well, to fit pretty much any set of game stats. My experience with many excellent gamers supports this. Given that fact, and D&D being a team game, it seems almost a no-brainer that you should pick game stats that make you game-mechanically effective, and build your interesting concept on top of that. (Or, conversely, make up a cool concept and then built it into an effective character — which is also eminently doable for the experienced gamer.)