Here goes a picture of some location in Eastern Europe. The plant with roundish leaves is Plantago and it totally belongs there.
So in the right upper corner is asphalt road. Left of the scene (not visible) is a publicly accessible well. People drive their cars to these scene to get water from the well. When they park on the lawn and then drive away from there they damage the lawn with the wheels. You see the results:
It was covered in grass (some uncool plants but better than dirt) for years and then perhaps two years ago this damage first appeared.
It'd be nice to have grass again on this lawn - it can be any plant that looks like grass and is suitable for a lawn.
This is public area - land belongs to the municipality. That might be formally illegal but most likely seeding anything or dumping some sand or ground there won't bother anyone. However restricting access there would most likely cause resistance and maybe even authorities involved.
How can this lawn be restored to some nice looking condition without restricting traffic to it?