Two-dimensional electron-hole gases in colloidal semiconductors have a wide variety of applications. Therefore, a proper physical understanding of these materials is of great importance. In this paper we present a detailed theoretical analysis of the recent experimental results by Tomar et al. [J. Phys. Chem. C 123, 9640 (2019)1932-744710.1021/acs.jpcc.9b02085] that show an unexpected stability of excitons in CdSe nanoplatelets at high photoexcitation densities. Including the screening effects by free charges on the exciton properties, our analysis shows that CdSe nanoplatelets behave very differently from bulk CdSe, and in particular do not show a crossover to an electron-hole plasma in the density range studied experimentally, even though there is substantial overlap between the excitons at the highest densities achieved. From our results we also conclude that a quantum degenerate exciton gas is realized in the experiments, which opens the prospect of observing superfluidity in CdSe nanoplatelets in the near future.