My therapist always started his session about 10 minutes after the hour and ended on the hour. I didn't really consider that starting late when I realized that was just the way he utilized his time. Sessions were full length, so it didn't bother me. I choose not to be too hung up on time in areas of my life where I have the flexibilty because as a teacher my life is literally run by a clock the rest of my day. I kind of like not even looking at a clock after I leave work.

Now the last minute cancellations would grate on my nerves.

You have to know what you are comfortable with, discuss your concerns with your therapist, and if things don't improve to a place that feels more secure, then finding another therapist is an option.