It's your pool and you can do what you want, but there's no way I'd run mine without both the skimmer and strainer baskets in place. I don't have any trees in my yard either, but I still get grass, leaves from the neighbors, insects, etc that blow into the pool. Although I try to keep it all skimmed off the surface and I empty my skimmer basket at least once daily, it's amazing how much of that stuff still gets to the strainer basket and into the filter. Besides, having to take the pump apart to clear the impeller because something got stuck is not hard, but is a real PITA. So....I would replace the strainer if it were my pool. But again....the choice is yours