The homeowner's association has a lot of power in the US, so it is inevitable that it will be misused and used incompetently. However only in the most close-minded and controlling of suburbs can you not plant a vegetable garden.
Simply a case of no, a lawn it must be?
... which means "protect interest of neighbors".
People like when their neighbourhood looks nice and is safe from snakes, bugs and mosquitos.
For most areas, it's aesthetic.
Here in the south-east, a short lawn will have no mosquitoes but a grassy area will have plenty (as in you'll get 20-30 bites in one evening outdoors), so that's a strong motivation.