The biggest risk is false findings for a lot of diagnostic procedures. A false finding may cause enormous psychological stress, but more importantly it usually causes further, more invasive testing, which may pose much higher risks than the original procedure did. It's real statistical risk, which individual patients emotionally often can't relate to. Eg. an MRI shows clear signs of a tumor, you consequently get an endoscopic biopsy through your stomach, or colon, and then happen to die from anesthesia, intestinal perforation, sepsis... The "tumor" turned out to be a cryptic but harmless extra intestinal loop. Sounds made up, but this sort of thing happens enough to make unnecessary diagnostic procedures more harmful than beneficial.

However, I do think the reason MRI aren't used more often is because they are fucking expensive to operate. They need to run more or less 24/7 to be economical, which means they are commonly not scheduled with slack for "optional" investigations.