I didn't use to think so, but a recent rewatch of S1 made me notice.
Think about how the character is portrayed:
- as an exceptional leader (especially in "The Enemy Within"),
- a legendary fighter (seriously, he gets into fisticuffs almost every episode, always triumphs),
- a ladies magnet of Rikeresque proportions.
There were entire episodes of season 1 also devoted to his flaws and frailties as a leader.
In "Naked Now" we see his insecurities about his love for command come to the surface.
The entire episode of "Enemy Within" is desiged to show off his deepest inner character flaws and how he needs to fight to balance them as a leader. Not sure how it shows him to be an "amazing leader" by any stretch.
Balance of Terror directly deals with his uncertainty and fears of making major command decisions. He openly admits his insecurities to McCoy.
He needs Spock to convince him of Mitchell's impending and inevitable danger in WNMHGB. He would have stumbled through the situation hopelessly until Gary destroyed the ship otherwise.
In Corbomite Maneuver his command decisions are continuously (and correctly) called out by McCoy as being biased and incorrect when it comes to his treatment of Bailey
In Conscience of the King, he allows his personal feelings and emotions to completely get the better of him.
That's just S1. We are not even getting into episodes like Obsession and the fact that the plots of Star Trek TMP, TWOK, TSFS, and TUC all deal directly with faults or flaws in Captain Kirk and the consequences of them.
Star Trek canonically states repeatedly that starship captains are amongst the best leaders humanity has to offer. Having Kirk be successful and a kick-ass officer doesn't make him a Mary Sue. In fact, the
entire basis of Kirk's character is that he is an extremely flawed and human leader who happens to OVERCOME and persevere despite those failings and weaknesses.
That's the opposite of what you're accusing him of being. That's the basis of a realistic and compelling character. A Mary Sue is a character who is devoid of weaknesses and flaws.
Just because the Trek universe at times reveres him and recognizes his accomplishments as an awesome bastard doesn't make him a Mary Sue
That is,
respectfully, absolute, inaccurate and unfounded bullshit.
Respectfully, of course.
And holy shit, if we are talking about squeaky-clean Star Trek characters, I can't figure how
KIRK comes up and not Picard. Prior to the recent CBSAA series, Picard was portrayed as a virtual shining paragon of every positive trait and characteristic that humanity might be capable of, to the point of it being sickening. And I still wouldn't even necessarily accuse Picard of being a Mary Sue.
And don't even get me started on Burnham. She's so flawed and fucked up that she started a war, went to prison, screwed up her foster brother and brought an evil dictator into our universe in a moment of weakness.
I'm not sure Mary Sue is the term you're looking for.
If you're looking for average, ho-hum and unremarkable characters, and not Big Damn Heroes in outer space, Fox recently put out a space series that has two seasons you might like better.
A real story involving Risa would either do what was done in DS9, or stay on track by having Vanessa Williams escort them to all the vending machines and dispensers for various antivesicants, antibiotics, antiviral agents, and other special liquids, pills, and/or gels to give us all hope that cooties won't ever be an issue in the future. It's hard to deny that dialogue encompassing that would be more intriguing than "Like how the common cold was eradicated"? (there's a line both TNTG and TOS used, except for McCoy it was in the context of how he might cure it... and Wesley or Beverly saying how they, like headaches, don't happen anymore. The level of cheese was remarkable... swiss cheese on the stovetop because it was a holey hot mess...)
and have boldly gone where nobody sane would dare and to try to defend it... (and still will 
In concept it's alien and meant to make the viewer feel uncomfortable...)
