Much depends on the pump. When they were available and there was no need for more flow due to water features, I regularly installed 1/2hp pumps on a pool that size with no issues keeping the pool clean and using a SWG if it was on the pool. A simple pool doesn't need anything more powerful, and they were California-legal. DOE regulations put an end to that.
They were always high-head pumps, like Whisperflo, Hayward Tri-Star, and, my favorite, the Waterway Champs-107S that moved more water than either of the others for the same electrical cost. Even used one on a 40,000 gallon, very old concrete-block pool, with only one 1.25" suction line (lily-pad skimmer) and one 1" return. Serviced that pool for over a year with no problems, just ran the pump 10-12 hours a day. It was a rental property and there was no way to talk the owner into a VSP.
Some of the solar pool pumps on the market use the Waterway wet-end on a solar motor and can move 40-50 gpm even on a cloudy day, plenty for a 20K pool. They are DC, variable speed motors that change speed as solar is available, so the flow may not always meet SWG requirements. Don't know what the OP has for a pump, so it may not be adequate.