You know there are plant-based ground covers even for wetter climates that better satisfy all your "plus" criteria at even less maintenance?

What lawns provide over those are mostly aesthetic and functional, not ecological.

Getting rid of the lawn, and with it the lawnmower, is the clear ecological choice, even if not always the right personal choice. No koan or paradox involved.

You are creating a false dichotomy. The alternative to a lawn doesn't need to be a hard paved surface -- you can have other plant life there such as wildflowers native to your locale and which survive without the massive supplements of water, fertilizer and pest control lawns often require. Such plant life has the same positive features in regard to erosion, etc. a lawn has without the downsides a mono-culture of grass often requires. Unfortunately some communities actually penalize people who don't have a lawn.

If you don't have an HOA or some city ordinance that requires you to keep it green year around it might not even take much water.

Here in the Pacific Northwest many of us never water our lawns. They get plenty of water from rain except in the summer. In the summer they go dormant. That turns them brown, but doesn't harm them, and when it gets rainy again in the fall they turn back to green.

May as well make the lawn mower require printer ink to operate while you're at it.