Is there an intuitive explanation for the maximal ergodic theorem?

Question

The maximal ergodic theorem states that for an $L^1$ integrable function the set $$E(f)=\{x : \max_n\left(\sum_{i=0}^{n-1}f(T^i(x))\right)>0\}$$ has the property that $\int_{E(f)} f d \mu \geq 0$. The only time I've seen it used is to prove Birkhoff's ergodic theorem by showing that the set of points where the $\limsup$ and $\liminf$ of the average of the interations of $T$ is not equal has measure zero. Does the maximal ergodic theorem say anything interesting or is it just a clever tool?