I currently have a therapist who doesn't change times, but in the past I have had a therapist who did, frequently. She was a forensic psychologist and she would sometimes get called up for emergency court cases. So for her it was unavoidable. But, knowing that didn't relieve the stress it caused me at all. My appointments were most often on different days at different times, and were subject to frequent changes.
My current therapist is exceptionally consistent with days and times, and has only once changed a scheduled appointment. The consistency makes an enormous difference. I think ultimately some therapists are committed to consistent scheduling and others are not.