Even if they managed to starve the yeerk out of her, it would have been almost impossible to contain her. She wouldn't have been able to stay in the Chee park, she was a little kid and she would have wanted to go home. They wouldn't have been able to stop her. And I don't know how a little kid could survive with the Hork'Bajir, they wouldn't know how to care for her, and she'd run away. The Animorphs would have to spend a ton of time taking care of her, and she'd probably die anyway. What would they do if she got sick or hurt? They couldn't take her to the hospital, Cassie's expertise and supplies would only get her so far.
For that matter, I kind of consider Karen being okay sort of a plot hole. If she were just some joe-shmoe no-one that happened to be a warm body, that would make sense. The yeerk peace movement could have gotten the yeerk from her, told her to be quiet, then carried Aftran back to the Yeerk pool, or carried Aftran in a willing host while the a Yeerk waited back at home.
But Karen was infested for a reason. She was watching someone, she was supposed to spy on someone, her father. The Yeerks would have noticed that lack of information. (Was that why Aftran was put on the spot in 29? I don't remember.) Either way, Karen was a dead girl walking, at least Marco would have merciful about killing her instead of her either going through being infested again (and giving away the animorphs) or her being assassinated by the Yeerks (which I don't think they would have done.)
Heck, they didn't even need to do the blood bank thing, all they had to do was reinfest Karen.
Honestly, when I first read it, it occurred to me that Karen was re-infested by another Yeerk of the peace movement, and she just lied and told Cassie she was free. It could close the plot hole.