Bitcoin public key cryptography is not based on RSA, but on Elliptic Curves, so the key is not a huge coprime (in fact ECC manages to achive a similar level of security with much smaller keys).
About why blocks are hashed, the reason is not to slow down anything, quite the contrary: it's to speed up verification that a block "follows" the other blocks in the blockchain. One does not need the hash to verify the transactions (in either the current block or the past ones), but since each block contains the hash of all previous blocks (in a compact way known as a Merkle Tree), one can not simply create a block "isolated" from the blockchain (taking as much time as needed) and then just "insert" it in the blockchain to win the reward - it's necessary that a previous block is known before a new valid one is created.
The "hard" part is creating a hash that satisfies the difficulty criteria. A concise explanation of the process is given in this answer. But one does not need to "reverse the hash" or anything like that for any reason.
