The actual computation done is not computationally useful. It only "secures" your bitcoins in the sense that an attacker has to put more economic input into their attack to match the economic input of the mining network. The act of mining does not even check whether the transaction is valid - that is done by the host that decides which transactions to include and the rest of the network deciding to propagate a mined block. Mining just churns through a single hashing algorithm to deliberately expend power. You could also secure your network by introducing trust and actually securing the trusted nodes, without having to create an ecological travesty.