Don't walk on the grass

It seems that people don't pay attention to "Don't walk on the grass" signs. Public spaces seem perpetually eroded by people too lazy and inconsiderate to walk on the provided paths. Public money is wasted returfing on a regular basis. And it seems to me that insufficient is done to prevent the erosion in the first place (other than the ignored "Don't walk on the grass" signs of course).

There must be a few available solutions, perhaps a breed of grass that is more resistant to trampling?

I also think it would be sensible to protect the edges of the grass (next to paths) as this is where erosion is most likely to occur. A 10cm high board along the edges of the path would adequately protect the immediate edge. Where people step over the edge protection, the erosion will be less significant as the grass can regrow from both sides.

I also wonder how effective it is to put down a rubber mesh where erosion is likely to occur. This allows the grass to grow through the holes, but prevents the damage from footfalls.