The popularity is based on simplicity and accessibility. You can easily find the indicator on any trading platform. Also, you don’t need to change any settings.
If you are familiar with other indicators, you know that most of them require changing the settings regarding the timeframe you trade. It’s not the case with the Alligator indicator.
Moreover, it’s easy to remember the signals the indicator provides. Just associate the indicator with an actual alligator and imagine its life stages.