While a first-principles calculation is often regarded a synoym for the density functional theory in condensed matter physics, the idea of “first-principles” is more deeper than that. It means that we assume nothing but the most fundamental truth (or something we believe), on which any falsification seems very unlikely at least in the near future, and arguments start from this point. For example, the existence of atoms, quantum mechanics, statistical mechanics are examples of the first-principles. On the other hand, DFT calculations are based on quite many other assumptions as a matter of facts.
Anyway, I believe that the first-principles approach is the very core philosophy in physics. There are numorous natural phenomena that hardly have an analogy or intuitive picture, such as the Bell’s inequality, superconductivity, the big bang, etc. If physicists had used only analogy or intuition, discovery of such phenomena would have been impossible. It required to write down equations, beginning from fundamental assuptions. And not to jump any steps but to expand equations line by line.
However, at the same time, so called a hand-waving argument or a comparision with a toy model can be very helpful in science too. When I give a talk, many people ask this kind of questions a lot:
You have explained this effect by blah-blah theory and blah-blah simulation. But is there an intuitive way to understand this (as an experimentalist)?
In fact, I also think hard to provide an intuitive physical picture whenever I prepare for a paper. But I want to say that making an analogy can be dangerous and one has to watch out not to overextend. I think it is important to know where is the starting point of this analogy (most physics analogy is based on a simple toy model, whose result is well-known — such as a harmonic oscillator, a two-level system) and where it fails as the system has more factors that are not taken into account in the model. In my opinion, using an analogy can achieve similar kind of works rather quickly, but it cannot really make a breakthrough which nobody has done.
Well, this thought came up to me while I was thinking about the orbital dynamics. Ananlogy of “arrow dynamics” is helpful, but I concluded that it cannot explain several important features of the oribtal dynamics. At the end, I decided to take a quantum mechanical description, for a reasonably simple but general model.