i specificaly will not sow grass because of this problem.
although i might change my mind for the paths that are to frequently walked on to keep anything else growing on. But not frequently enough to not have weeds.
I am gonna try and sow Turf clover
talked about it here
It’s a nitrogen fixer (although in a lower amount then others)
It’s supposed to stay smaller than 6 inches, even without mowing.
It’s more of an experiment. So treat my “info” with that in mind. Or maybe run a small patch as experiment yourself