I support this idea. Maybe straw could grow in the plains biome like how cacti grow on the desert biome and how reeds grow next to water. It would grow at the same rate and look similar to reeds but are yellow and can only grow up to 2 blocks tall. They would be used to make these hay bales/straw blocks in the same combination as your wheat recipe. I also support the attracting mobs. But to be more in-depth it would have a 15-block radius and friendly mobs would have an increased chance (10%?) to spawn within 15 blocks (only z and x coordinates; cannot have increased spawn rate on blocks above or below the book that the hay bale is placed on) of the hay bale.
Well, so far the wild tall grass only takes up three different damage values, which leaves us with 13 open slots for more grass types. Hay could generate randomly on the map like any other tall grass. However, upon breaking it would always give the player hay (instead of giving the player a chance at collecting a wheat seed). Hay could also be one of the plants to randomly generate when bone meal is used on a grass block.