I think all of these are good arguments for doctor's offices but physio is different, in my mind.
The physio I used to have scheduled her appointments very close together, like 15 minute intervals. That's because she would do about 15 minutes of treatment then set you up doing weights or muscle stim or some other activity that was part of your treatment but didn't need her to be there.
OP, if you'd waited no more than 5-10 minutes while the physio set someone else up, I would say that was normal. More than that? The office doesn't properly schedule their appointments. It is unfortunate that you don't have another option. I think your idea of going after work and taking a book or craft you can do is a good idea.
I once made a doctor's appointment for an annual physical for 8:00 am, the first appointment slot of the day. At 8:30, the doctor still hadn't arrived and there was no explanation or ETA from the receptionist (I don't think she knew). So I re-booked and left, since I normally start work at 8:00. And was really annoyed because I would have to be late again another day. One other time, I had an appointment with this doctor and the receptionist came out and announced to the large waiting room crowd that he'd been called to the hospital and had no idea how long he'd be. We could wait, if we liked, or we could reschedule. That was ideal - I could make an informed decision. And one time, I was in the waiting room and he called me in about 5 minutes after my appointment time. I blurted out 'You're on time!' The entire waiting room cracked up. But boy, was I embarrassed about my foot-in-mouth disease. I did end up changing doctors because I was sick of always waiting at least 30 minutes for every appointment. My new doctor apologized if you waited more than 15 minutes.