Being free is great. Being energetic is great. Why would I want to minimimze free energy?

Free Energy, with capital letters, is a concept from thermodynamics, which you hint at when you mention, in passing, "minimize entropy". This is also known as "negentropy" a central concept in information theory.

I do not recall why thermodynamicists came up with the term Free Energy, but it seems to me using it out of context like this makes the explanation of an otherwise perfectly sensible Principle harder than necessary.