No one what's to read the enterprise logs of Mary Sue. Not only do character flaws give your characters potential for growth, as you've said, but they also make them relatable and well rounded. While they might not be needed to drive the conflict of the story at hand, it will certainly drive the conflict of a scene; at least meaningful conflicts.
I agree. Even in humour, a perfect character has to be so far over the top (Buckaroo Banzai, for instance) as to be laughable just because s/he is perfect at absolutely everything.
To me a flaw that sticks around is something like they may have a hard time with short memory but still fantastic at long term memory. Maybe they had a stroke and their face is still paralyzed. The person can't stop stuttering when they speak. They can't stop their hand from shaking if they have a tick. A person can change their thought patterns, actions, and behavior, but they can't change their core personality. Like in the book people code and color code personality, Red's, blue's, yellow's, and white's do the same thing regardless of who they are. On the Meyer's brigg's Infj V. Estj. Their personalities clash. They can both be personally developed and reach self-actualization but you can't beat the core personality out of them. Red's Vs. Blue's they both want power and control but have different motivations behind it.