My assumption was wrong.
It turns out that there had actually been a lot of grass fires started because of sparks, heat, etc. that came from parking (and idling) on dry lawns -- and those grass fires had spread to buildings, neighboring lawns, entire blocks. To prevent this, they prohibited people from parking on unpaved surfaces.
I am sure if enough people in your community don't like the law, you could talk to your local representative (City Councilperson) and see about having it changed.
You could also pave your entire front yard and tell the city to stick it.
I think blight and trespassing are also reasons for these laws. If it’s legal to park your car on your own lawn, then it would also be legal to give a friend or guest permission to park on your lawn, and it would also be legal if you didn’t happen to be at home during the entire time the car was parked there. From a practical standpoint, it then becomes impossible to police the problem of people parking their cars on other people’s lawns without permission. In densely populated areas, and in the vicinity of commuter train stations, sports stadiums, etc, this is often a real problem. The only way to keep the neighborhood from descending into chaotic disregard for property rights is to have an ordinance that allows police to ticket to any car found parked on a lawn.