They didn't forget - it's addressed in detail. They are advocating "small scale"

The low efficiency is mainly since air heats up during compression. This waste heat, which holds a large share of the energy input, is dumped into the atmosphere. A related problem is that air cools down when it is decompressed, lowering electricity production and possibly freezing the water vapour in the air. To avoid this, large-scale CAES plants heat the air prior to expansion using natural gas fuel, which further deteriorates the system efficiency and makes renewable energy storage dependent on fossil fuels.