Why analysis of Aloha protocol uses Poisson distribution?
IMO, the biggest reason is that Poisson distribution is more tractable mathematically. Some experimental studies claim that it does follow Poisson. However, there are also other experimental studies show that it does not. 

Mathematically, Poisson distribution can be viewed as the approximation of binomial distribution under certain conditions. However, it is not the rationale behind the Aloha protocol. 

As a mathematical model, you should consider your own scenario carefully and decide whether to use it or not.