They don't send phones out fully charged because there's a risk of it exploding in transit (they aren't nice to packages in the mail room!) and as a consumer its your responsibility to take care of your phone and it's set up.
As for refurbished phones- that's what mine is. All my phones have been refurbished and its really no different than a new phone. They don't send it out without rigorous testing and a new battery.
Your battery issues are either from you messing up the battery life (patience is a virtue) or it could possibly have to do with where ever you're located.
I'm from Washington state, pretty moderate climate. When I visited Minnesota last summer (really hot!) my battery life sucked horribly. So depending on where you are that might be mucking up your battery also.
At this point I would recommend you go buy a new battery and set it up properly. Don't put the new battery in until you go to bed, let it charge all night. Next day(s) run it until its so dead you can't turn it back on, then charge it all the way up while it's off. Don't touch it, just let it charge. Your battery will have a great life.
Oh! And make sure your battery setting's are on "battery saver" and that your screen is on "auto" brightness. Moving backgrounds will shorten your batter life.