Why wouldn't you use CT scans to detect cancer in everyone?

What you are looking. Every radiology test like ct mri, angiograms, radio isotope scans, sonograms, pet scans, sonograms etc has a specific indication. All cancers cannot be detected by ct alone, for scattered small deposits of tumor( metastatic) pet scan is used, some of the bone tumors MRI is better, costs risks& benefits to be considered finally physiology and physics of tumor decides which is needed.
False positives. Every test has false positives, including ct scans. If we were to scan everybody, it would reveal far more false positive findings than cancers, expose every body to unneeded and harmful radiation and cost a bundle. In short, this would not be an effective preventive strategy.