The conclusion that energy is more fundamental or easier to have an intuition for has been the case since, what 100 years ago? It certainly was when I studied physics 20 years ago.

But he doesn't need to go into quarks for that. Simply comparing the masses of protons and neutrons (+ electrons) to the mass of an atom shows they're different. There's a little bit less mass due to the lower energy of the bound nucleons. Quarks certainly make the effect more dramatic though.

A more practical objection to using mass is that nobody can agree on what the word means. Does a photon have mass? Yes or no, depending on if you're thinking of relativistic or rest mass. If you call it energy, there's no ambiguity.

If I could recommend he change anything though, it would be the horrible mixture of units - MeV/c^2, atomic mass units, and grams. The author surely has the time to convert them all to the same unit so the reader can easily compare them. That would eliminate the need to explain Avogadro's law. It's a completely redundant complication of chemistry and has nothing to do with the fundamental concepts he's focusing on.