In microphotoluminescence measurements at room temperature on Al0.2Ga0.8As/Al0.4Ga0.6As multiple quantum well microdisks, we observe a large number of whispering gallery modes in a remarkably broad energy range of about 250 meV. This is in contrast to microdisks containing InGaAs or GaAs quantum wells, where typically only one or two whispering gallery modes are observed, but similar to the behavior of microdisks containing self-organized InAs quantum dots. We conclude that impurity levels below the recombination energy of free electron-hole pairs inside the alloy quantum wells lead to an efficient internal broadband emitter with low absorption.