I follow your train of thought Roger, the problem in a lot of cases is the water movement in pools is really poor so it takes a long time to actually remove anything. We move into the area of water science. Filtration is a dilution principle, The first pass of the water through the filter is only around 63.2% of the water, 2 turnovers is 86.5% of the water, 3 turnovers is 95.0% of the water, 4 turnovers is 98.2% of the water, 5 turnovers is 99.3% of the water. Baring in mind that only the water close to the surface is actually going into the skimmer. If the flow/turnover rate in the pool is low because of bad system design, if it was ever designed rather than just happening. Considering people only run their pumps for 8-10-12 hours a lot of them are only filtering 70-80% of their water and in the shut down state dirt continues to enter the pool so they seldom get a really clean pool.
Faced with that people add the flocculent to hurry things up but the pool industry does not know how to add flocculent or doesn't care. If you flocc then run the pumps as the floccs go through the pump they get all smashed up again which allows them to pass through a lot of filters. switching off the system allows the floccs to sink and be hoovered out but they cloud the pool unless you are really gentle when moving the vacuum head. The correct way to add flocculent is after the pump and before the filter, this requires a mixing process and a reasonable length of time for the flocc to form. That way you use around a 1/5th of the flocculent but get far better results.
This is why the water flow system of a pool should be designed by someone who understands and knows hydraulics and water treatment and not by a block laying gardener/general builder.
People run their pumps for too shorter time because of the cost, that area has now been addressed and so running a pump 24 hours a day cost's about the same as a conventional setup running for only 2 hours. The cost savings will pay for the additional changes and go on to save a considerable amount of money but also produce far better water quality and less maintenance time.