Today we're going to be discussing the strengths and disadvantages of a min-maxed character. The core concept is that TTRPGS are based on overcoming challenges, and you want a character that does well in that area without breaking it. I will try to keep this as system-neutral as possible, but it will help if the reader is familiar with an ascending AC and hit system (higher AC/roll to hit is better).
We're going to take a look at some examples of fighters both on 2.n and in 5e, so the next few paragraphs are going to be pretty dense with stats. To keep things simple, let us work with a basic fighter. Furthermore, let us start out with two examples of fighters that are both totally unworkable, one that is a terrible fighter and one that is way too good of a fighter.
2.n Example
Wrath is our poorly optimized 1st level fighter. His core 6 stats are 3 3 3 18 18 18, he doesn't wear armor, and he attacks with thrown daggers that he is not proficient with. His AC is 6, his attack is -8, d4-1 (to-hit, damage), and his HP is d10-2.
When fighting against a goblin, Wrath would do pretty poorly. He'd need to roll a 20 to hit, and even then he'd need 2 hits to kill it. On the other hand, the goblin would hit him on a 6+, and kill him in 1 hit. Wrath sucks. He'll die to one goblin. We're not even going to bother looking at how he'd fare against other monsters.
On the other end of our spectrum, we have Rain, our super min-maxed level 1 fighter. Her core 6 stats are 18/100 18 18 3 3 3, she wears full plate +5 with a shield and a +5 sword she is specialized in. Her AC is 31, her attack is +9, d8+13, and her HP is d10+4.
When fighting against a goblin, Rain would do very well. She'd need a 5 to hit, and always kill a goblin. On the other hand, the goblin would need a natural 20 to hit, and need 3 hits to kill which would take ~30 rounds.
When fighting an ogre, Rain would need a 6 to hit, and 1 or 2 hits to kill. Since she gets 3 attacks every 2 rounds, she'll probably kill an ogre in 2 rounds. She'd be hit only on a 20 and be killed in 2 hits, making it very unlikely an ogre would kill her. She's going to wreck any ogre she comes up against.
Against a hill giant, Rain would need an 8 or higher to hit and kill it in 3 hits. The giant would hit her only on a natural 20, and kill her in 1 hit. I'd still put my money on Rain, but now it's quite possible that she'd get killed.
5e Example
Wrath is our poorly optimized 1st level fighter. His core 6 stats are 3 3 3 18 18 18, he doesn't wear armor, and he attacks with thrown daggers that he is not proficient with. His AC is 6, his attack is -6, d4-4, and his HP is 6.
When fighting against a goblin, Wrath would do pretty poorly. He'd need to roll a 20 to hit, and would need 7 hits to kill, but be hit on anything other than a 1, and be killed in 2 hits. We're not even going to bother looking at how he'd fare against other monsters.
On the other end of our spectrum, we have Rain, our super min-maxed level 1 fighter. Now, you could go Her core 6 stats are 18 18 18 3 3 3, she wears full plate +5 with a shield, a +5 sword, and the Heavy Armor Master feat, reducing incoming damage by 3. Her AC is 25, her attack is +11, d8+9, and her HP is 14. Rain is an impossibly amazing 1st level fighter.
When fighting against a goblin, Rain would do very well. She'd hit on anything other than a 1, and always kill. The goblin would need to roll a 20 to hit her and would kill her in 7 hits, which in this case would be ~140 rounds.
When fighting an ogre, Rain would hit on anything but a natural 1, and kill an ogre in 4-5 hits, which if she action surges can be done in 3 rounds. She'd be hit on a 19+ and be killed in 2 hits, or about 20 rounds. Again, super easy for her.
Against a hill giant, Rain would still hit on any attack other than a natural 1, and kill her enemy in 8 hits. The giant would hit her only on a natural 17+, and kill her in 1 hit or about 4 rounds. She's not so great here, but she could do it with a little luck.
Return to normal discussion
It's pretty clear that Wrath is useless and never any good. It's also clear that against the usual monsters you'd be fighting at level 1, Rain is so strong as to be almost invincible. Even against ogres, Rain is going to win out over and over again. You have to have a 1st level character fight a hill giant to get to a battle where she might lose.
And this is our problem. When you have a super-mega character like Rain, the only things that challenge you are the things that will kill you if they can hit you at all. Combat becomes stale. There's little room for fun when the outcome is predetermined or if you're likely to be totally dead from a single attack.
In trying to make a really good combat character, we've ended up making a character that is boring for combat.
Now, Rain is not a possible character to make at level 1 (unless you've got some crazy story you're running), but the same principle applies to characters you can make. If your skill at a task is too high, that task becomes boring. If you can kill any monster, pick any lock, climb any wall, or talk your way out of any situation, those challenges are over. There's not much to engage with there.
Nobody likes to play characters like Wrath who are no fun in combat, but Rain is equally as boring in combat. You might as well just be a deity when dealing with small monsters, and big monsters that actually might give you a run for your money are frustrating because it's a one and done deal.
Conclusion
Playing a strong character is fun! Playing a fighter who can really wade into the enemy and dispatch foes left and right makes for a great story. We just have to be careful not to push it too far. We have to remember that the fun of the game does not come from victory, but from overcoming challenges. The victory must feel earned or it is not rewarding. A quest kill all the chickens on a farm would be an easy, but unrewarding victory.
There's nothing wrong with optimizing (min-maxing) a character for combat, as long as the character you end up with is enjoyable. If you want to play the sort of character who can kill a goblin in a single blow, build yourself for damage, but keep your AC down. If you want to be an amazing shot with a bow, build for that, but also engage in melee combat.
Our characters need strengths and weaknesses to be fun.