Perhaps I am being a bit thick here but I can't see the difference between this and a flower bed. If you walked all over a flower bed, you would crush all the flowers...wouldn't the same happen here ?
My lawn is a bit like that, plenty of daisies and buttercups et al..found a little viola in it the other day so now replanted that in case the mower gets it. I can't see how a flower lawn will stand up to heavy wear..nice to see but not really tough enough methinks.