Firstly I would like to point out that the total energy is actually conserved and can't become greater or lesser. What we are talking about here is the potential energy of the system.
Secondly, I think that this is a really fundamental question and, although very interesting, such questions tend to end up in philosophy. Thirdly I will try my best to give some answers.
Usually minimum potential energy principle is viewed (at least that's the way I see) as a basic principle of the world. You can compare the minimum potential energy principle or electrostatic forces with a force that you maybe know a little bit better:
- Why does gravity make masses attract?
- Because that's the way it is, it's fundamental law of nature.
I don't know if you believe* in gravity, but I do. And I believe in energy minimization aswell.
However, if you want an explanation, it can also be explained by other laws. In this case it's the maximum entropy principle you mentioned (also known as second law of thermodynamics). This law tells that the system will try to maximize it's entropy. The consequence is that all the energy will try to convert into thermal energy (heat) thus increasing the entropy.
Now you run into next question - why maximum entropy? Well, this is once again usually viewed as a basic principle of nature's mechanisms, but it can actually be derived from statistical physics. However, by doing this, you might once again run into some principles of physics and mathematics ad infinitum so in the end you'll have to believe in some principles or at least think in the "if this is correct, then this is what follows:" way.
-*- by using the concept of belief I talk about believing a formula or a law without formal proof, but it is proven by experiments that the formula works. Even if a principle is not the principle on which nature bases processes, it surely gives the same results.