(new) bitcoins can't be the reward of a project like seti@home, because to find a valid bitcoin in the first place (to mine it) takes that much computing power.

(new) bitcoins can't be the reward of a project like seti@home, because to find a valid bitcoin in the first place (to mine it) takes that much computing power. Now that some valid bitcoins have been discovered, those cryptographically valid 'coins' (hashes) can be used as money. Such as a reward to SETI@home users. But whoever takes the time to mine that unique, distributed blockchain (the consensus' transaction log of all bitcoins) has to choose to give the SETI project those unique bitcoins. The process of rewarding a good deed and the process of mining a safe blockchain are independent, and can easily take many thousands of volunteer computers, respectively. If you can design a system that generates a cryptographic secure chain of the collective transactions of volunteers computing unrelated problems... you should publish the design.