As someone who lives in Norway (permanent resident) I'm quite surprised that Sweden is so bad. A couple of years ago I visited my GP complaining of a small hard swelling on my foot. he said it's probably just a ganglion and that he could fix it if it didn't improve by itself but that he would like an MRI scan first to check exactly what it looked like. It was obviously not even slightly urgent but I still got the scan with a month. In Norway such scans are normally performed at a specialist company (Unilabs in this case) even though it is all paid for by the health national service (except for about 150 NOK egenandel, that's about 15 USD copay)
I'm in the US and have had multiple MRI scans happen either the same day as an appointment or the next. Compared to that, even a month seems pretty long.
It wasn't urgent, I wasn't in pain, there was no rush. If it is sufficiently urgent it's possible to get an MRI within minutes of arriving at a major hospital.
https://unilabs.no/