Our yard is about 3" of top soil on top of basically solid clay. When we moved in a little over a decade ago I tried taking on the dandelions, but I quickly pivoted to planting clover. Now we have tons of the stuff, fewer dandelions despite no chemicals (not that I really mind them anymore), and our yard smells fantastic in mid to late spring when all the clover is in full bloom. Tons and tons of bees, crickets, etc. We re-did a flower bed and intentionally planted swamp milk weed and red crocosmia in it. They look fantastic together and the bees absolutely love it, not to mention the butterflies.
But yeah. About English ivy. Been fighting that stuff for years…