My pool owner's manual contains a copy of the National Swimming Pool Institute's
Suggested Minimum Standards for Residential Pools Compliance by January 1, 1974.
Section 9.1 states, "A recirculation system ... shall be provided for complete and continuous circulation of water through all parts of the pool designed to provide a minimum of two (2) turnovers in twenty-four (24) hours."
Note that that doesn't really say you should run the system continuously, nor that you should try for two turnovers per day, just that the system should be sized that way.
Codes for commercial pools say they should be run continuously.
It's not easy to find authoritative web references for residential pools, but a few stated running the pump for one turnover per day.
This
one contained the interesting statement, "It has been proved that at least 7 complete turnover periods are needed before 99% of the pool water has actually passed through the filters."
I'd also note that at the point in time that the pump is turned off, the water is still circulating for some time so some mixing would still be occurring. Also, even when the water becomes still there is diffusion mixing occurring.
In the end I guess it just comes down to "guess and test", with the ecological and financial goal of finding the minimum time required. Perhaps start with one turnover per day and reduce or increase as needed. But what will indicate the "as needed"?