That’s not the idea. The computational problem is simply a proof of work—you create a specific, verifiable string, with a changeable component greater than 256 bits, then hash that string using incrementing values until you find a SHAsum less than a certain value. Knowing a random, short preimage for each possible hash doesn’t help you there, because those will not allow you to create a verifiable string with the correct hash.
That’s not the idea. The computational problem is simply a proof of work—you create a specific, verifiable string, with a changeable component greater than 256 bits, then hash that string using incrementing values until you find a SHAsum less than a certain value. Knowing a random, short preimage for each possible hash doesn’t help you there, because those will not allow you to create a verifiable string with the correct hash.