Urgent care would not be urgent if you had to wait months. Hang out with a few elderly people who actually need to see specialists more than people like me. Over the years, I've heard plenty of stories from people I know waiting multiple months to see specialists.
Yeah, and specialists are "usually" not available via urgent care. If not for the like of urgent care, specialties would be worse. The fact that it takes so long for such access is still a demand and supply problem at the end of the day, no way around the knowledge bottleneck - fixing that means shifting demand to different, more plentiful, supply (doing that soundly is not trivial, but likely easier than attempting to multiply the specialists, depending on the specialist). ERs are expensive because they have to have certain specialties "on tap" 24/7, among other reasons. This is not a unique problem of any single health-care system.