This is frequently true in the USA as well. My provider's dermatology department is pretty backed up and couldn't make me an appointment for an excision until November. Fortunately it's not urgent.
Somewhat related: a couple years ago my spouse had cancer, and the doctor could do surgery either 5 days after our insurance was changing companies, or 2 months after that, those were the next two openings. The insurance said that if we proceeded with the surgery, without the new insurance company giving us approval, but they couldn't start approving it until the insurance started, and the pre-approval from the other company didn't give us anything. We finally decided to go ahead with it and take on the risk of ~$70K if it was denied. Which we decided to do rather than my spouse spending a few months worrying. Turned out that was a really good call, because when they did the surgery it turned out that instead of the expected slow growth, it was actually growing extremely fast. That was probably the difference between it being fatal and it being treatable.
The US system is far from smooth.
You should see how long their surgery departments are backed up!
(For those not in the know, out of network means costs to the patient are much higher).
https://www.chiefhealthcareexecutive.com/view/hoping-to-see-...
ZocDoc isn't reflective of availability as a whole. It has a lot of depth in certain areas, like dentistry, dermatology, and primary care, and less in other specialties. Many of the providers are not physicians, they're NPs and PAs. Perfectly qualified for certain kinds of issues but not others.
ZocDoc is also, obviously, working only with the providers who are willing to pay for new patients, such as newer practices trying to build a patient base. An established practice that is booked out for the next two months obviously isn't going to use such a service.
Finally, you're not considering insurance and continuity of care.
So yeah, in an urban area, you can probably find someone to see you sooner than later if they're in network or you can afford to pay, and you're okay with seeing someone you might never see again or with whom there might not be continuity of care.
https://benchmarkcanada.org/Governing_Healthcare-Wait-Times....
The US does far better than the UK and Canada.