Precision public health requires research that supports innovative systems and health delivery approaches, programs, and policies that are part of this vision. This study estimated the effects of health insurance mandate (HiM) variations and the effects of physician utilization on moderating colorectal cancer (CRC) screening rates. A time-series analysis using a difference-in-difference-in-differences (DDD) approach was conducted on CRC screenings (1997–2014) using a multivariate logistic framework. Key variables of interest were HiM, CRC screening status, and physician utilization. The adjusted average marginal effects from the DDD model indicate that physician utilization increased the probability of being “up-to-date” vs. non-compliance by 9.9% points (p = 0.007), suggesting that an estimated 8.85 million additional age-eligible persons would receive a CRC screening with HiM and routine physician visits. Routine physician visits and mandates that lower out-of-pocket expenses constitute an effective approach to increasing CRC screenings for persons ready to take advantage of such policies.