It's not that MRIs suck at cancer. They provide fantastic structural and functional data.

The problem is the specificity of the results and the prior.

A full body MRI by definition will provide detailed views of areas where the pretest probability for cancer is negligible. That means even a specific test would result in a high risk of false positives.

As a counter point, MRS means that you can now MRI someone's prostate and do NMR on lesions you find.

Lets say someone has lower urinary tract symptoms. And is 60 years old. An MRI could visualize as well as do a analysis that would otherwise require a biopsy. With the raised prior you can be quite sure suspicious lesions are cancerous.

Similarly for CNS tumours. Where fine detail. Subtle diffusion defects can mark csncers you couldn't even see if you cut the person open.

No sensible doctor would give you a whole body CT unless there was a very good reason. That very good reason is probably "we already think you have disseminated cancer". That pushes the prior up.

And less so for a PET/CT. Lets flood you with x-rays and add some beta radiation and gamma to boot!

The danger of an unnecessary CT/PET is causing cancer, the danger of an unnecessary MRI chasing non existent cancer.