According to Box and Jenkins, ARIMA is a linear non-stationary model. It is an imporvement over ARMA.

In my experience, ARIMA might be favored over other methods because of its flexibility.

You can achieve far better results if you decompose your signal into simpler components and use simple linear models to forecast each time series and then combine them into one forecast.

So, it is initially easier to work with and it can handle non-stationarity if there is homogeneous nonstationary behavior in the time series.

There are many scenarios where ARIMA model fails. e.g. if there is heteroskedasticity in your data, it cannot be modeled with ARIMA.