[Aqwis]

Another possible factor is specialist availability. As I assume is the case in all public healthcare systems (and in some way or another, e.g. through price differences, in private healthcare), some specialties have a glut of physicians while others have a real scarcity. I've personally experienced having to wait many times longer for a neurologist than a gastroenterologist, even though the issues my GP referred me to those specialists for were about equally serious, simply because there are so many more gastroenterologists available (relative to the demand) compared to neurologists (be it because too few neurologists were trained 5-40 years ago, because neurological issues have gotten more common, because GPs refer patients to neurologists more often than they used to, because neurologists may be more likely to go into private practice than gastroenterologists...).

With medical imagery, you don't just need to get to get the MRI, CT or whatever done, there often needs to be a specialist available who can decide how (or if) to treat you based on the results (the exceptions being very routine stuff that a GP can often handle the treatment of, e.g. common bone fractures; or screenings where a negative result is expected in 95%+ of cases, such as if you present with a headache and your GP wants to make sure you don't have brain cancer).

In the public healthcare system we have where I live, if my GP thinks I have a problem that's serious/non-obvious enough that an MRI would be useful (and it's not a highly routine issue as previously mentioned), the waiting time for that MRI will depend almost completely on when a specialist in the relevant field (or subfield) of medicine is available – otherwise, the MRI won't be up-to-date, etc. The MRI scans themselves tend to be done by private labs that are subcontracted by the public healthcare service anyway, and (as you'll learn if you ever book a private appointment with one such lab) these labs have lots of capacity. MRIs in themselves are cheap enough (it would surprise me if the public healthcare service paid these labs more than $500 per MRI on average, a pittance compared to the cost of a physician*) that there is no point for the public health service to queue up MRI appointments for months if they manage to book you an appointment with one of their own specialists.

The details vary between countries, of course, but if a public healthcare system in a rich country has so few MRI machines (and doesn't subcontract out outpatient MRIs to private labs) and/or are so penny-pinching that they find a speedy $500-$1000 MRI to be too expensive, then I would say those problems seem to be relatively easy to fix without changing anything fundamental about how the country's healthcare works.

*) Although this may not be the case if the physicians in your country earn less than, say, $30,000 USD on average – the cost of technical equipment matters less the richer a country is.