Your insurance is almost certainly a factor here, in that they require you to see a GP before escalating the issue to a specialist (one of the most highly-paid, I might add, who might have a busy schedule also). But what you've described is not uncommon for any insurance company.

Other countries with "universal healthcare" also have times consuming referral processes and wait lists for stuff. But they have it worse because there are more people seeking service, and less providing it (because profits are capped). I've heard plenty of stories of people in those countries dying on the wait lists for things that sound urgent or mundane, like appendectomy surgery. I even heard a few where people with ordinary problems like trouble walking were offered euthanasia. You should do a bit of research before you whine too much.

So, what would solve the problem of having to wait? Ultimately more supply of service providers, less demand, or an unlimited budget to pay for the scarce ones that exist.