YABVU
My clinic (though not a GP) ran very late today because one of the patients turned out to have a serious problem which required me to break very bad- and llife changing news- to the patient and then arrange immediate admission to the ward from clinic.
What would you expect I do in that situation- chuck them out of the consulting room after their allotted time ran out, regardless? Imagine if you, or a loved one, were in that position- what would you want?
I imagine you would want the doctor to spend the time needed to get to the bottom of their problem/take time to break bad news sensitively and thoroughly/ explain proposed treatment etc.
The reason you can't be seen if you turn up late is that if everybody who turned up late was seen in order, the clinic or GP surgery list would be running even later. If I am running late, I will usually try and squeeze people in, but some days that is just not possible if they are very late.
GP's have 10 minutes per patient- that is not a lot of time if the patient has a complex problem, or if it bad news or if the patient is unwell. I understand from friends who are GP's that it's not unusual for patient's to come with a number of problems and expect them all to be dealt with in 10 minutes. It's not unusual for patients to come in with one problem, then mention something else which the Dr thinks "I need to deal with that as it could be serious". Again- in that situation think what you would want the Dr to do if it was you or your loved one? Deal with the problem or ignore it so they run to time?
I understand that it can be annoying when the clinic or GP surgery is running late and you have things to do, but more often than not it can't be helped. Have a bit of patience- and some good grace!