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-...
Elsewhere in the body, MRI is less useful, and isn't really a workhorse as it is with neuroimaging. (Except maybe joint imaging.) Most emergent problems are detectable via those other cheaper, faster, & less onerous technologies.
Your guess about size is also likely correct; the positioning of the antenna/coils and relation to the magnet are very important (especially with a weak magnet) and much more challenging/variable if you're thinking about the range of abdomen sizes (for example) versus head sizes.