I dislike sentences like 'you still have to wait months for an exam or years for surgery'. Depends on the exam or surgery.
- Blood test: wait time (after your 12 hour fast) is likely 15-30minutes in most of Europe (even eastern Europe. I should know, I do one every 3 month).
- pet-scan/x-ray: at most a few hours if your area is truly underserved, in my experience, less than an hour (but I needed it 4 times, so it might be small sample size).
Specialists will make you wait for sure if it doesn't sound life-threatening for deeper exams, and especially exams that requires surgery, but the only example I have on hand is my mother's boyfriend who got his in less than two weeks, and his cancer removal surgery was planned within 3 months after the tumor biopsy (you need to change your diet at least a month before surgery to prevent complications and improve healing, so the true delay caused by wait time is ~2 month). They also explicitly said that if his cancer was more aggressive they would have given him a month to prepare according to my mom.
But yes, in Europe especially, convenience surgery can take a year (my intern lips and teeth took 17 months) (and you pay a bit out of pocket), when in the US you can be done within days.