> Why does the template transaction need to be signed in step one and passed back and forth so many times? What is wrong with:

It isn't passed "back and forth so many times".  It works exactly as you proposed, with the only difference is in "Step 1" the sender uses a *signed* transaction instead of an unsigned one.  This is an important anti-DoS/anti-spy tactic, as it proves the sender actually owns those inputs and if the protocol is not followed to completion, the transaction can be dumped on the network.