Interesting characters have memorable strengths and weaknesses and in a game I would expect the mechanics to reflect them.
In fact, I'll go as far as to say that min-maxing your ability scores is fantastic for roleplaying and creating memorable characters, because it gives them both prominent strengths and weaknesses. Take Minsc, for example - the pinnacle of physical perfection with a hamster-sized brain.
First, let me say that I understand the desire to make a mechanically strong character. In fact, I almost always do. Of course, that said, I completely understand where Ixal is coming from. And I can see how min/maxing negatively impacts the enjoyment someone else gets from solely roleplaying.
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But regarding the quote above, I'd argue that min/maxed characters aren't exactly "memorable." The reason being is that they all pretty much look alike. These are typically carbon copy builds, or very close to. They're using the same dump stats; they're hiking up the same stats; they're using the same weapons and feats and charting out all the same progressions.
You're right, naturally there's nothing memorable about the 1000th character following the same very specific min-maxed build. I made the mistake of using the terms min-maxing (always picking the best options out of all with some specific goal in mind, e.g. 'highest damage per turn') and optimizing (creating a concept and making it work the best you can) interchangeably. Or at least I think that's what the right definitions are. Are they? Does anyone even know?
Anyway, I was thinking more of the latter. For example, let's say your concept is a charming enchanter wizard who's a master of mind-manipulation, reading people and navigating high-society intrigue. As you begin to 'optimize' your build, you figure out you need your Charisma and Wisdom to be reasonably high in addition to Intelligence, which leaves little room for the physical abilities. This prompts you to leave Strength and Constitution in the dumpster, creating a character who's the smoothest talker that ever walked Faerun and folds like a paper crane under hydraulic press as soon as words fail them. Clearly not the "best" built character ever, but definitely memorable I'd say.
