I think you only see the three mentioned because they are what were originally published in the "core" rules. The Arcane Companion's/Spell Lists/Professions came later.
Also, they can develop the other three realms spells, but they will pay more for it (i.e. 'other' realm). For a logical reason why, that's simple: Balance. If you want a philosophical rationale then they are learned and cast differently, just as the other three realms are learned and cast differently. If you want to say "But Arcane IS all three realms" then I would say "But it is a much more raw form of them, lacking some of the finesse of the others, which is why it's failures are more spectacular."