A good point, and worth keeping in mind, but that's not the question I'm asking. I specifically want to know about personal tolerance toward mechanical effectiveness.
Imagine you're playing in a serious game, you've put a lot into your character (personality and backstory), you've explored and saved the day and made friends with NPCs, and you've lost one or two (PC) allies to nefarious enemies. You've been playing the campaign for six months and everyone is around level 10, when you get a new player to the game. The new player is playing a half-elf barbarian (also level 10) with a greataxe.
When the character joins the game and the new player describes their appearance, they mention that they have a Strength of X, which catches you off guard because you really would have expected their Strength to be higher, and now you're unsure about whether this new character/player is going to work out. It may not have been presented that way, but you can't help but feel that the character is going to wind up as comic relief, which doesn't at all fit the serious/gritty tone of the game you've been playing so far.
How high could X be, for you to still have this reaction? For the purpose of this question, assume the game isn't using feats.