Yb:YAG thin-disk (TD) technology has enabled construction of laser/amplifier systems with unprecedented average/peak power levels, and became the work-horse of many scientific investigations. On the other hand, for some applications, the narrow emission bandwidth of Yb:YAG limits its potential, and search for alternative broadband TD gain media with suitable thermo-opto-mechanical parameters is ongoing. The alexandrite gain medium has a broad emission spectrum centered around 750 nm, possesses thermomechanical strength that even outperforms Yb:YAG, and owns unique spectroscopic properties enabling efficient laser operation even at elevated temperatures. In this work, we have numerically investigated the power scaling potential of continuous-wave (cw) Alexandrite lasers in TD geometry for the first time. Using a detailed laser model, we have compared the potential cw laser performance of Yb:YAG, Ti:Sapphire, Cr:LiSAF, Cr:LiCAF and Alexandrite thin disk lasers under similar conditions, and show that among the investigated transition metal doped gain media, Alexandrite is the best alternative to Yb:YAG in power scaling studies at room temperature. Our analysis further demonstrates that potentially Ti:Sapphire is also a good alternative TD material, but only at cryogenic temperatures. However, in comparison with Yb:YAG, the achievable laser gain is relatively low for both Alexandrite and Ti:Sapphire, which then requires usage of low-loss cavities with small output coupling, for efficient continuous-wave operation.