Well, first you have to ask what advantage you get by turning everything off before shutdown. I don't see any. Next, is there an advantage to having everything off at start-up. Again, I don't see one, because most cars shut off the blower fan when cranking. Does a CX-5? I leave everything as I last used it at shutdown and I can't remember if the blower runs when cranking.
If your battery can't start the engine with the blower on, you prolly need a new battery.
If your battery can't start the engine with the blower on, you prolly need a new battery.