I have been charged a cancellation fee from my psychiatrist, and that I didn't mind because it was 100% my fault, I totally left it off my calendar and failed to show up or call.

My therapist would never charge me for a missed appointment if I was ill. Heck she wouldn't if it was something I forgot if it was a one time thing, when I started with her she did warn me that if there was repeated missed appointments without notice there might be a missed appointment fee.

Just wait until your therapist is ill and then you can ask for a doctor's note.