I'm not sure why it doesn't sit well. Why does an electron attract a proton? Because negative charges attract each other. Well why is that? Because that's how it works. But why? Because it's how the universe works. See where I'm going? It doesn't matter how far we go down or how much we explain, someone can always ask why. At a certain point you simply have to accept the fact that that's just how it works.
Don't confuse the different types of energy. The thermal energy contained in a book on a table is most definately not zero. The book has zero gravitational potential energy UNTIL it is either pushed off the table or the table is removed or whatever.
These "ideas" ARE what we observe and measure. The equations we used are 100% based upon observation of how the universe works. There is absolutely nothing abstract about them. The only thing abstract here is the idea that Energy is "something".