What about the drain(s) from the cockpit, do you close them as well, when you leave the boat?
Good point. Most cockpit drains will only have one hose/seacock per drain, whereas, the engine seacock will have many connections and components that can fail... the strainer being one. Therefore, you will decrease risk the most my leaving drains open, and everything else closed.
As to the OP. He gives good advice. Check everthing that is under the water line often.