It is hard to define "most competitive".
But since the OP mentioned "limited athletically", of all the top names mentioned, you have to admit that Bird was very limited athletically. Which means that his accomplishments were driven more by "competitiveness" than athletic ability.
Magic, Jordan, Kobe, and LeBron all were FAR more athletic than Bird.
Then you look at Bird's practice habits. Off the charts.
Bird elevated the players around him. Without Bird, it is VERY unlikely that Robert Parish, Kevin McHale, and Dennis Johnson would be in the NBA Hall of Fame. Maybe Bill Walton just misses out too, without his late-career renaissance playing with Bird.
And to top it all off, Bird was a world class ****e-talker. He would call his shot, and then make his shot. He was taking deep threes before it was a thing, then he would rub it in his opponent's face.
Bird was competitive on a level that few have ever come close to, and yes, Kobe came close, particularly as a ****e-talker. But, seriously, ask yourself which teammates Kobe elevated to a Hall of Fame level. NOBODY. Jordan elevated Pippen, without a doubt. Magic can get credit for Worthy. Zeke pushed Dumars to the HOF level. (LeBron - nobody).
But nobody elevated his teammates any greater than Bird did. Basically got THREE other longtime teammates to the Hall of Fame.
And all while wearing crappy shoes.
OH, and And AND Bird played lights-out defense, something Kobe never did.