Shredding them up with a mower simply increases their surface area, so they decompose a lot faster. (It's a natural, yearly cycle.) This coming winter, the dead leaves will protect fragile roots (which are usually near the surface) from the cold, and plants will green up faster come spring with the extra nutrition.
Owen Yost, in addition to blogging, is a Landscape Architect emeritus from here, who‘s worked in north Texas for over 30 years. He is a member of the American Society of Landscape Architects (ASLA), International Society of Landscape Architects, the National BirdFeeding Society, National Wildlife Federation and the Audubon Society. He was honored with a Lifetime Achievement award by the Native Plant Society of Texas. His design office is at email@example.com