You can. And the cost is higher than almost anywhere on earth.
You can get them quickly in most places with a publically funded healthcare system, it’s just that a priority patient is very very sick and you never want to be that person.
Granted, anything you find in that reading won't be accepted by your physician or insurance company, so it's more of a checkup for you and you alone. And most scans will find something anomalous. We're all asymmetrical and lumpy. so take that as you will.
Surely that it isn't the norm? Where do you live that the (I assume government run) health system dismisses evidence when its collection wasn't sanctioned by official channels?
But I was really speaking more broadly, about healthcare in general. There are only so many doctors, so many MRIs, so many heart surgeons, so many this or that. Giving everyone a bunch of extra money so they could pay the current prices doesn't do anything to address the scarcity, so everyone flush with those subsidies will just bid up the prices - which is exactly what happened.