I don't like wasting anything either. I don't think the cover has anything to do with algae. At least without it you can see any algae starting and do something about it. My opinion only. Not using a cover lets you fire the pump to circulate and vacuum as necessary until the last possible date. Just because the pool is uncovered doessn't mean you have to run the pump. Once swimming season is done for me, like tomorrow, I have no fixed schedule for the pump. When I get enough crud on the bottom, I'll vacuum. I watch the FC and pH and if I need to tweak I'll run the pump for a few hours to circulate. This may be just a couple times a week. Whenever necessary.
Al