Engine run-ins, after ground-checks, also require lots of constant power-for-a-time for ring break-in.
If memory serves correctly (was about 15 years ago) for a Lycoming 360, it's 75% power for an hour, then alternating 75%-65% power for a couple more hours. Clearly on a new/reconditioned engine you'd want to be over non-tiger-territory too. Mineral oil and no continuous lower-power ops (e.g. circuits) too for 50 hrs then oil change. Or something like that. In a training aircraft, first 3-4 hrs are essentially non-revenue-earning and next 47 hrs are cross-country-limited-circuits.