Entities externalize state that can vary over time. So it isn't f(g) but f(g(t)). Time (and hence mutation) really does exist, whether it is implicit or explicit.

It is only easier to reason about when the data you give the function is limited. You can always pass the world into the function and take it as an output, then it no longers matter. Effect systems are also possible with objects as well, they just aren't a feature of functional languages.