The problem is that these reminders usually focus on waiting time for appointments rather than one specific thing. We could be talking about several timeframes at once: when you must be scheduled after calling the clinic, when a doctor should see you, how much time can pass between diagnostic tests and a specialist consultation. For emergency care it's hours, for urgent care it's a day or two, for planned care it's usually up to 14 days, though it depends a lot on the region and the doctor's specialty.
In practice these timeframes get violated pretty often, and here's the important part: it makes sense to complain, but you need to know where to complain. You can go to the insurance company (the one that issued your OMS policy), contact your regional health ministry or the regional ombudsman for patient rights. The key thing is not to just wait around to get scheduled a month later, but to ask the receptionist right away why the timeframes are being violated and request a written response.
The catch: even if you were scheduled on time, that doesn't guarantee the doctor will actually see you when they're supposed to. Queues, a doctor calling in sick, office maintenance - these are all common reasons for running late. If appointments keep getting postponed, that's grounds for a complaint, because that's not an emergency situation anymore, it's a systemic problem with that specific facility.