First, as
@Whizbang Dustyboots stated in the second post of this thread, if everyone at the table is having fun, no problem. The character may be "bad" in terms of optimization or even thematic fit, but sometimes a player and group can make that work and make that fun. Nothing to fix. If no harm, no foul. No need to pull out the hat-o-blame. But in the spirit of the OP...
As a GM, I would blame myself. I blame myself because that means I can do something about it. So, where did I fail?
1. Maybe it really is the system...but still my fault.
If it is poorly designed and makes it easy to create "bad" characters. My fault for choosing to run this system. Or my fault because I should know the system well enough to help players avoid the bad-character trap. Obviously, if I'm new to the system, I'm more likely to fail to catch these kinds of issues, no worries. I'm at least experienced enough to catch when it is becoming a problem, helping the player create a new character, and exiting the old one and introducing the new one in a way that fits the adventure/campaign. Or at least isn't too jarring.
2. Maybe it is the player creating a character that isn't a good fit for the game I'm running. Still my fault. Poor session 0. Failure to make character creation a group activity. Forgot to review and discuss character builds and backstory before starting the adventure/campaign, when it would have been easier to discuss with the player. No problem, I've learned to not passively avoid potentially difficult conversations. That leads to other unhappy players and the adventure/campaign--and possibly the group--falling apart.
3. Maybe its the adventure/campaign. This is more likely with homebrew. But sometimes the campaign or adventure you want to run just doesn't jive with the system. The incongruity becomes more obvious with some character choices more than others. Opps, my bad. Time to decide if the campaign/adventure concept is more more important than the system or vice versa. May need to take a break to restart with a new rule system or start over with another adventure/campaign.
I just don't see the point in blaming the system. I chose to run it. And there is not a system I've played yet that is immune from the bad-character problem. Rarer in some, more common in others. Easier to avoid and address in some, much more work to find preemptively or fix after the fact in others.
I don't see much point in blaming the player. That's just a normal social dynamic you have to navigate in any game. The only exception is if the player somehow insists in playing a character that is not working for the group and we are not all enjoying the game. Like any problem player scenario, you either have to kick out the problem player, kick out the players that are having problems with the bad character, or ditch the adventure/campaign and starting fresh with something everyone will enjoy.
So, the game master's fault. My fault. Sorry. Let's fix it and game on.