One advantage of focusing on puzzle transactions is that finding (and taking) those funds presents no moral dilemma. It's meant to be a reward.
please clarify - how is finding/taking funds (essentially stealing) found to have no moral dilemma? and why would stealing be a reward?
or am I misunderstanding and there is no stealing being done and these are just free funds floating out there?
Yes, my understanding is that you are supposed to try and brute-force an N-bit key for a reward of BTC. So, if you found a 50-bit key, you'd get 0.05BTC.
It's now getting so difficult that I don't think keys 58 and up (until the larger claimed ones) are going to be found soon, unless it's just pure luck. The search space is massive. I can crack a single DES key (I search the entire 64-bit space) in less than a day, but there are additional more expensive steps to finding a valid private key. So just keys/s is not really enough; other optimisations need to be done. The distribution of rewards according to work with the LBC was a good idea.
So, essentially my understanding is that while you don't own the key, a) it's been made deliberately findable (at least for smaller keys!), b) there's a hint on where to search for a key for the BTC reward, and c) the transaction was created in a curious manner indicating this wasn't just any type of funds transfer.
I think we can make a reasonable inference that this is a puzzle, and if you get lucky and do some real work to find a key, you get some BTC.