A little dividend from the COVID epidemic is that folks who walk behind a gas mower can wear their handy masks and filter out some of the dust and particulate matter when they are mowing.
I still have the lawn that came with the house, but I will not use herbicides or fertilizer on it. I leave grass clippings and top-dress with compost. I dig dandelions and crab grass (and compost them). All-sorts of ground covers are left to their own devices, but (except for a small area where I have planted some perennials, including sweet woodruff) ground covers are mown along with the grass. The two ground covers which I would say are most rampant are self-heal (Prunella vulgaris) and creeping charlie (Glechoma hederacea). I enjoy chipping sparrows and juncos when they come to eat in my lawn. If I had nothing but bluegrass in the lawn, I doubt that there would be as much good fare for them. I also have ugly toads, red-bellied snakes, common garter snakes and little copper-colored frogs in the lawn. It is more fun to walk in my grass than people might think.