You're basically saying that competitive is bad. I disagree. Any personality trait can be bad, depending on the person and the situation. I know someone who is extraordinarily competitive, and the nicest person in the world. And as for tenacious, I guess you could call this person tenaciously competitive.
There's a huge difference in someone who uses competition as a measuring stick, and someone who wants the competition to be "less than him (her)".
I've seen just as many tenacious whack jobs in my life as competitive whack jobs, probably more. Now that I think about it, I've seen a LOT more tenacious whack jobs than competitive whack jobs. Often times tenacious people are just trying to be competitive in a game that no one else is playing.