The number 1 is very real, assuming the universe is quantised. And any number where the equation x = 1x is true is also very real, since it's basically an extension of the number 1. By "real" I mean exists as a self consistent non-human concept in the universe, not the mathematical concept of "real numbers". The number 1 is not useful, it's fundamental. Without 1, there is only 0. That means a universe that doesn't exist.

There's nothing arbitrary or even philosophical about quantum energy levels.