If you re-hash the exact same block, you will get the exact same hash.  That is useless.

To get a different hash result you HAVE to change the data you are hashing.  Generally this is done by modifying a piece of data in the block header called a nonce.  Incrementing the nonce results in a slightly different block header which then results in a completely different hash.

Miners are so fast now (and difficulty is so high), that they typically try every possible nonce without finding a valid solution.  Then the miner HAS TO modify the transactions and rebuild the block so they can try again.

So miners (or pools) already have to rebuild the entore block MANY times before a solution is even found.

There is no "making progress" towards a solution.  Every attempt has as good of a chance of being the right solution as every other attempt.  Think of it like rolling dice.  If 2 people each roll a die until one of them rolls a 1, are all the previous rolls "wasted"?  Has anyone's chances of rolling a 1 gotten better (or worse) just because a 1 has (or hasn't) been rolled yet?