Wanting to have a character who is really good at the thing that you want them to be good at isn't wrong. But both systems and playstyles mean that having a character that is too optimized (either to 'do all the things' or so focused on a single scenario that they can do nothing else) tends to create some problems, in my experience. Some have already been mentioned, but also:
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The player doesn't have fun when their character is outside of their 'niche', and torpedoes the 'nonfun' scene to get quickly to whatever it is their character is good at. ("Court is boring, so my barbarian punches the King.") Or they just tune out, which can be almost as bad, if it's a small tabletop group.
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Other players start to tune out when the MinMax character does THEIR thing, because they feel like they have nothing to contribute to the situation. Ideally, in my opinion, every RP scene should have something for every PC to do (whether they choose to DO IT or not is up to them).
I believe in niche protection - I think every PC should have something to contribute to a group or game that other PCs can't easily replace. But with a group of minmaxers, that can be taken to too much an extreme where you're almost running four separate campaigns, where only one player is engaged at a time. Some systems almost demanded this (Early Shadowrun, particularly, had the game everyone else was playing, and then the game the Decker was playing), while others incentivize it (especially systems that tend to set difficulty levels for tasks high, and have high penalties for failing for tasks), so it's not something I tend to blame on players.
A lot of us have been trained to make the most maximized character we can have. And in MU*s, I notice this is promoted by people who ask for/demand a certain skill level before even letting you into a plot or giving you RP. Hell, even on ARES, with F3S - which is NOT a particularly 'high threshold' system - I've had to shut someone down because they wanted to find the mechanically "best" person to take on a plot scene, rather than base it on RP factors.