By 'output' I (think) I meant the output we get for the energy used by the miners.
You seem to be saying that The Miners have to verify transactions to claim their reward? When you say "which are all verified separately" - you mean verified by the same miner who publishes the block? If so then the bitcoin network as a whole benefits from their energy use.
On the other hand, I see your point that the make-work is not intrinsically linked to transaction verification. But my understanding is, its the difficulty of the make-work that protects the block-chain from being hijacked by ..er... 'the bad guys', whomever they may be.
So, the whole thing kinda makes sense, and the 'make-work' is like an energy commitment that keeps the whole thing integrated. The assumption being, the total commitment of all bitcoin users will always be greater than the commitment of any single attacker/attacker group.