It makes sense for Lake Travis to be not a constant level lake as I guess it is good in times like this for it to be low to hold all this water as it fill ups. But why are Lake Austin and LBJ constant level?
Lake Travis is designed to be a reservoir for flood control. The other lakes are designed to pass water from flood reservoirs to downstream areas. They're constant level to pass the water down smoothly, and not all at once.
There are other reasons as well. Some lakes are designed to be recreational lakes. These lakes are generally constant level lakes as well. (that or they aren't designed for the drastic swings of say Buchanan or Travis). There are also lakes that have been built for the express purpose of being a source for drinking water.(supply water for human 'consumption' which of course is used for more than drinking) Many lakes were built for at lease one purpose even though almost ALL are used beyond their primary purpose(es).
Travis and Buch are large and have a lot of capacity making them suitable to hold large volumes of flood water. The other Highland lakes are smaller and their capacity is immaterial for the purposes of flood control therefore their role is just to move water down river.