Assume for a second that we found a proof of work algorithm that had all of the good properties of sha256, but was also useful for SETI and maintaining world peace.
Now suppose a group of miners collectively have more than 51% of the hashing power. In which of the following scenarios are they more likely to collude to double spend via a 51% attack:
A) When the proof of work algorithm is something like sha256 and is only useful for securing the bitcoin network
B) When the proof of work algorithm helps find aliens and maintain world peace in addition to securing the bitcoin network.
In Scenario B, if BTC lost all of its value due to a 51% attack/double spend, miners' hardware would still be valuable because although it couldn't mine bitcoin, it could still find aliens and maintain world peace.
In Scenario A, if BTC were to lose its value, miners' hardware would go down with it, due to said hardware's uselessness for anything other than mining...