The idea that during La Niña the tropical Pacific is storing energy--"charging like a battery"— and during El Niño it is discharging energy seems like a reasonable analogy for the result of the ocean and atmosphere processes that drive the ENSO pattern phenomenon. But climate scientists aren't just interested in the result; they want to understand why and how things happen in the climate system.

You say a battery analogy allows us to dispense with all those messy and "complicated atmospheric dynamic processes." But a simple battery analogy would provide no explanation for all the parts of the system that we can easily observe. It doesn't explain why "the battery" is located in the western tropical Pacific and not the whole Pacific. It doesn't explain why the battery would ever discharge as opposed to endlessly accumulating energy. It doesn't explain why there is no equally strong battery in the tropical Atlantic Ocean or the tropical Indian Ocean, etc. 

In other words, if we ever want to understand why and how the battery discharges--which we do, since it has such a strong influence on seasonal climate—we have to dig into the complicated stuff. As the quote usually attributed to Albert Einstein says, "Scientific explanations [theories] should be as simple as possible...but not simpler."