I think they're harder to manage when you do include grasses, although the flower heads above and against the grass seeds look so very beautiful....
Our neighbour tried to create a hay meadow, bought a seed mix. First year there were quite a few nice flowers but very little grass. He asked us to make hay for him, which we did as late as feasible - very late August, I think it would have been, or maybe 1st or 2nd Sept - the bales were solid and no-one could lift them more than a few feet! We had to use a tractor with front-loader to help collect them and bring them in, no-one could stook them! Much to everyone's surprise, the "hay" was spectacular - all the stock loved it and it smelled and looked beautiful.
Second year, very few flowers, thick unruly grasses. Not sure why, except that because of the timings and logistics, the hay may not have been wilted and turned as much as would have been ideal for shaking all the flower seeds out - but then most of the flowers had seeded long since.
Hay-making was not attempted. I'm not sure what to expect this year...
Another neighbour has a 'wildflower meadow' (patch of grass) in front of their house, and it is gorgeous. They mow it once, very late (October) every year, and it comes and comes again year after year.
A nature reserve hay meadow on the moorlands a few miles away has the very rare globeflower and melancholy thistle. I have yet to manage to see the latter in flower, but we usually manage to catch the globeflower. I don't quite know why, but it is so beautiful you almost want to cry when you look at it.