What makes sense in one location does not work in others. I mow what grows in the areas that are lawn. We have gardens of significant area but still have grass. I don't use any fertilizer or weed killers. I rarely have to water. Sometimes we get dry spells but like I said it is rare and water here is plentiful, too plentiful. I don't bag my clippings just let the mower chew them up and drop them. I bet I am sequestering carbon. You are lucky if you can control the weeds with occasional applications of mulch. I put down mats under our mulch to stop the weeds and still every few years I have to remove the mulch and mats and replace the mats as the weeds have grown through the mats and the mulch and I still have to weed the gardens a lot. The grass is way easier and cheaper to maintain than the gardens. All I have to do for the lawns is cut it once a week, edge and trim.
What you suggest might be great for some people but not for me.
Tim