Wait times differ greatly depending on where you are and what kind of care you’re seeking. I moved a couple of weeks ago, and decided to try and deal with my hot-flashes issue. Last Tuesday I opened an issue with my clinic, and I got an appointment for Thursday that week. In my old town I had a previously recurrent health issue that had me waiting for four months to see someone.
Sadly politics plays a part too. In the U.K. for example, if you’re a trans person and you’re seeking medical care your case will bounce around endlessly, and you might not ever see the care you need. Same procedures for cis-people can be organised really fast though. Philosophy tube made a really good video on the issue.
It’s also not uncommon for clinics to be understaffed, and the workers to be overworked. This obviously can also lead to issues. I’ve a friend whose cousin died because they didn’t recognise his type of cancer quick enough, despite him seeking help for it frequently. They honestly didn’t really look for it until they faked him passing out, prompting them to take him seriously.