Who said she wasn't, the whole point was that she doesn't own one yet
The heart that is strong and true shall win the keyblade. Even though Sora was trying to find Kairi and Riku, Riku distanced himself from him. Told him how he was able to find Kairi and he was going to save her, and that he did more than Sora ever could because he was floundering with his friends Goofy and Donald. They both acted differently for their own goals, but it was only an instance that Sora would lose his keyblade to Riku because his heart simply wasn't stronger than Riku's at that point. Now sure maybe it is speculation whether Sora had grown a weak heart, or Riku's just got stronger, but there's evidence through the game where Riku tries to give Sora self doubt. He basically taunts him for diverting a path to his true friends in his mind.
Neither was the keyblade for Sora, how do you think this changed. Again you need a strong heart to wield a keyblade. If it accepts you, it's yours.
It's not speculation upon acceptance of the keyblade. If someone accepts you to hold a keyblade, and the keyblade accpets your heart, it will happen. If you have a strong heart to hold a keyblade it will happen, but if you're not it's master, the master will simply summon it back from your own hands. This happened between Riku and Sora in Hollow Bastion, so if the Masters heart is weaker than that of a strong hearted person the keyblade may possibly choose that person more fitted for it with previous acceptance. Both Riku and Sora are keyblade masters now. When Riku gave Sora the acceptance of holding his keyblade to attack Xemnas he did, but there's no struggle between keyblades here, because they both respectively have their own, so the struggle between hearts is the difference here, because there's no need for it.
Kairi was chosen by Aqua in an unconditional situation. It doesn't mean she can't own a keyblade, she simply doesn't have one. Their are different means of being able to wield a keyblade, but the common one is through having a strong heart. If Kairi finds a keyblade, and it accepts her as her own, then it's hers.