Imaging in general has an important role in screening for certain diseases, and in some cases is already more important than physical examination. This mainly depends on how "well" physical examinations can detect an illness, the characteristics of a particular imaging study (cost, radiation exposure, etc), and the characteristics of a disease (prevalence in a population, potential benefit of early detection/treatment). So in short, for MRI to replace physical exam and/or lab testing in screening for a particular disease, the cost needs to come down or the benefit should outweigh the cost.

Prostate cancer screening in general is no longer officially recommended by the AAFP as a rule [1], but if a patient decides to opt-in to screening, the "assay" (PSA) is preferred over a digital rectal examination, which has been shown to be increasingly useless in the detection of prostate cancer. MRI doesn't currently have a role in prostate cancer screening, but Prostate MRI has an increasingly critical role in diagnosis.

CT colonography is currently a viable option for colon cancer screening instead of colonoscopy, though colonoscopy is still considered the gold standard.

Chest CT is currently recommended to screen for lung cancer in patient's that meet certain criteria (age, smoking history).

Mammography is obviously the workhorse of screening for breast cancer, rather than physical examination. But MRI is recommended as a screening mechanism for certain patient populations with very high risk of breast cancer (e.g. certain BRCA mutations). The small population, high prevalence, and benefit of early detection combine to make this a viable option.

[1] https://www.aafp.org/family-physician/patient-care/clinical-...