Without double hashing, finding the nonce would be easy because one could calculate the working variables up to everything in the block header except the nonce, and then use a SAT/SMT solver to solve for the nonce which sets the concatenation of the working variables less than the target.
Since the nonce would be in the last 512-bits of the message, SAT/SMT solving for just that last set of updates to the working variables in a manner that the result is less than target would be quicker.
So Satoshi added another hash to mess up the resulting working variables further.
This Satoshi bloke seems to be a bigger weasel than anybody thinks. Combine the choice of double hashing with his choice of the non-tainted curve, and one could be certain that he engineers cryptographic schemes.
There aren’t many who do that. His UK spelling means he is either working for the British intelligence agencies or he is truly John Galt.
P.S. Satoshi means wisdom in Japanese. So either he knows he is wise which is likely. And then he reads manga, watches anime and had to learn to Japanese. Since that trend isn’t old he can’t be that older than me. — pardon my wild speculation.