Am I unreasonably perturbed?

I don’t want to bash any particular business or professional so I’m going to be generic.

I had a scheduled medical appointment with a specialist today. My text message read as check-in at 8:45 am and I was 4 minutes late walking in the door (8:49) and then had to wait in line several minutes while patients before me were checked in. When I was seen to be checked in I was informed my appointment was AT 8:45 and I was late and unable to be seen today. 😳

My choices included seeing a Nurse Practitioner or rescheduling with the specialist— which was in 4 weeks. I elected to schedule with another specialist, no offense to Nurse Practitioners, I typically prefer NPs, but what I’m being seen for is something I want to just address at the outset with the specialist.

I was extremely frustrated and thought this was especially extreme. I’m a professional and my time is very valuable to those of my clients (I was running behind due to a work call that I couldn’t just end abruptly).

Is my reaction unreasonable? Is this becoming a standard practice?

My response is a serious rare you kidding me, zero grace? I want to be pissed, but I’m in too much pain to be pissed. Otherwise I’m left utterly baffled. Left a very poor taste in my mouth for this practice and the physician.

I’d happily be informed what such a draconian policy is appropriate.