Grasses have an ability to conserve water in their leaves. They can also absorb carbon dioxide without losing any water. Grasses are well equipped to deal with rapidly changing weather and strong winds, the kind that sweep across plains, praire and steppe environments. It would be also true to say that herbivores adapted to eating rough grasses, as well as seeking out the sweet grasses. The teeth of the Late Pleistocene mammoths were designed to grind down grass and their mouth's housed a greater number of teeth than earlier mammoths with a more elephant like diet (including wood and leaves of trees). In the last Ice Age savannah or steppe existed in a wide swathe below the ice sheet. This is herbivore territory – and the mammoths required bulk vegetation in order to survive.
See www.sciencenews.org/article/genetic-switch-offers-clue-to-why-grasses-ar…