The purpose of mining is to secure the blockchain.

Orphans are not part of the blockchain.

If there was a reward for producing orphans, it would draw resources away from the blockchain (main purpose of mining).  At the very least, people would be lax about optimizing their setups and we would see more orphans as result.  In the worst case, we could even suffer attacks.

Also, it adds unnecessary complexity to the software.  An orphaned block is a block that does not follow the rules of bitcoin.  Even if everything else is correct, it was not based on the latest valid block at the time of creation.  But there might be more problems with the block.  We would need a special (exceptional) verification function to find out.

And last not least:  Properly verified, an orphan still represents "proof of work", although not for work towards the main blockchain.  However, it wouldn't indicate any "speed of hashing" anymore as we have now.  Even the slowest miner can produce an orphan, given enough time.  Under your hypothetical proposal, we'd only know that work has been done.  We wouldn't know whether it EVER had the slighest chance to be actually useful for the blockchain.

There is nothing to reward unless proof is shown that the blockchain is now more secure than before.