Touch of Power discussion

As I understand it, Avry can transfer aches and illnesses from sick people into herself. Then she experiences it and heals, faster than a normal person would.
If she takes in a lethal disease, it will kill her all the same. If Avry can only take in treatable diseases, why does she not simply allow the patients to heal on their own?
Are the services of these healers really as necessary as the book stresses?

Avry heals a lot faster than 'normal' people. so the disease might not kill her, cause it heals fast, but it would kill someone else cause of major blood loss etc

I'm a little surprised this question was asked given that it's explained, litterally, on page 1. The little girl was going to die but Avry needed only a nap to clear away the danger of the disease from herself.