In RSA you need to pick primes, if you pick random numbers RSA doesn't work. But the elliptic curve public key systems work with more or less arbitrary numbers so you can just use any random number as a key. Some magic numbers like zero may not work depending on the algorithm, but

(a) you can exclude those explicitly with a tiny amount of effort

AND

(b) probability of picking any such number for a 128-bit key is insignificant