>>2731907Creeping thyme could maybe be OK. Perennial Peanut could maybe work. But both of those are non native same way most landscaping grass is.
Creeping Phlox is good for some areas here and there, but look grass lawns are ubiquitous for a reason. A well kept grass lawn is ideal, fairly low maintenance, beautiful when kept correctly, good for high traffic, uniform, etc. It's the best option.
I get people want to be different and all but the best thing you can do is keep a nice well kept grass lawn and then go in with native specimen hardwoods and then layer some flowering understory trees in below them. Then do beds along borders and fences and fill them with native perennials and shrubs as you please. If you have space beyond the yard harrow it up and spread a native wildflower/grasses mix for your region.
I keep a manicured lawn around the house with native hardwoods and a few natibe lines here and there. Native understory shrubs and trees underneath and alomg fencerows I make rectangular English style hedge squares from dwarf yaupon hollies and then inside of the rectangles I make raised beds with native perennials. Crossvine on the fences.
Beyond the yard I'll pick a few little paddocks and pastures here and and let the red sorrel and toadflax come in on its own in early spring- it's beautiful. But once It plays out by about mid april- I mow it and start fighting the Bahia Grass all summer with the rotary mower. I'm a big fan of Southern Sugar Maple as an undersea native landscaping tree (if you are in the South east).
Anyways- you MUST mow and spray if you have sizeable areas you are working with, things will simply get out of hand if you don't. knowing when and how to time it and having some restraint is the key.