There's nothing particularly special about the constants. They needed a set of n constants to work with and the "cube root of first n primes, truncated" scheme is a "nothing up my sleeve"[0] construction. If they'd used magic numbers with no obvious generation scheme, you'd be left wondering if that was done as a way to put a back door in place.

[0] https://en.wikipedia.org/wiki/Nothing-up-my-sleeve_number