I am very late to this one. (oops)
I would not wait 2 hours to see a doctor unless it was a specialist and I'd been told that that might happen. I think 15 minutes is tolerable but not great, and half an hour would really piss me off and I'd expect them to acknowledge, apologize, and promise it wouldn't happen again. I can't take a half day off every time I have a doctor's appointment. It's one thing to have a specific situation and it's another to overbook so it happens consistently.
As for delivery, I went to a group practice (all women), so even though I had my main doctor, they rotated me through everyone during my pregnancies so I would be familiar with everyone just in case it was someone else's turn. I get it; they took turns being on call, which seems fair to me. With my son I got my regular doctor but not with my daughter, but I'd already met her and been examined by her. It wasn't my preference but I didn't think it was unreasonable that they trade off being on call.
My Gp here in town at one point 2 hours was a standard wait time they actually encouraged you to call at your appointment time rather than come in to see how long the wait was. A co workers husband was still waiting for a 11am appointment at 5pm one day. It was a pain because I always get appointments after work so as not to inconvenience anyone so i was often still at the doctors at 7pm with a very hungry child.
My GP in my home town is never on time but I will wait for her because she is so good.
The doctor had lost the other doctor in his practice so he was still trying to see the same amount of patients a day. I have few choices here, most doctors have closed their books to new patients and the one I know of who will take new people I refuse to see because I have seen him once and know his reputation and he is not a good doctor. My GP in my home town only works two days a week as well so getting into her can take awhile and she doesn't take new patients really, she has a following who go wherever she is working, including when she worked at an indigenous clinic.
We just changed family doctors because of the wait times and the fact our old GP was never available. If I called to book an appt it would be at least 2 months down the road, she only worked part time and she relied on a locum to manage her patient load. Plus, she was starting to lose her mind, I think. Once, when I mentioned that the intimacy in my marriage was waning a bit she said "Well, you have to kids so you never have to have sex ever again if you don't want." Like, what kind of doctor says that?????
Anyhoo, our new doctor will take the kids the same day if they're sick and DH and I can get in with an appt the next day if we're sick.
I was thinking about this thread while at our new walk in clinic last night. They have a really cool system where you can text in, and they will put you in cue, then they will text you 10 min before your appointment, so you dont have to sit around the waiting room for hours. Just thought it was really cool and wanted to share. Also, I have learned that if you just walk in, with a cute or crying baby (as I did last night), they will fit you in at the front of the cue. Its not like anyone can tell if the waiting room is empty :)
Our pediatrician has special hours reserved for "sick" visits, they don't book appointments during that time so they can take the kids who need immediate attention without having to disrupt everybody else. They always use it, that's for sure.