If we were all optimal posters, optimised for reaching a consensus, I fancy this thread would have reached a conclusion a lot sooner. But, alas, we are are all human* - we do not always act optimally and it is hypocritical to castigate others for not doing so either.
A feature of 5e is that every character, however fiercely optimised by its player, has a Flaw. Optimum play involves, inter alia playing to one's characters' flaws to gain Inspiration dice. In that way, players are rewarded when their characters act sub-optimally for some particular purpose. Not for being stupid, but for being human. This illustrates that best play by the player is not necessarily the same thing as choosing the most effective activity for the character to display. Sometimes, it is better play to have one's character display ineptitude. But not all the time, obviously.
The OP used the phrase "purposefully inept" and went on to say he didn't approve of such things. I think he meant to say "deliberately" or perhaps "gratuitously" inept but, actually, "purposefully" in the sense of "done for a good reason, to achieve a particular goal" is close to what I was describing above.
Whilst I would agree with the OP's sentiment that unco-operative behaviour by a player is a bad thing, I don't agree with the implication that sub-optimal behaviour in a character is automatically reprehensible. If it serves to further the narrative in some entertaining way, then it is indeed justified and does not represent anti-social play by the player; on the contrary he may thus be fulfilling his obligation to entertain his fellow players around the table.
To give a single example: a barbarian whose signature move is to grab a lighted firebrand and use it as an improvised weapon may score fewer hp of damage than if he used a greatclub, but if it scares the pants off clumps of animated plants that infest his homeland, who is to say that it is wrong? If you play such a character, I would applaud, not condemn you, and just quietly prepare a few frost spells as back-up for when fire proves ineffective. Good team players do not inveigh against each other's shortcomings, but adjust their own behaviour to counterbalance them.
In short, I would advocate that characters be fairly effective but not strenuously so, and the degree to which they are not, should be part of their charm.
* With the possible exception of me - after an unfortunate accident I was reincarnated as a small furry keyboard in a far-distant galaxy, but I can reasonably claim to have been human once so I type with some authority, at least.