Unless you’re worried about not being able to feed your puppy frequently enough, I would not leave food out all day. There are many benefits to actually feeding your dog, rather than having the food out all the time.
Actually feeding your dog
– helps prevent the fats in the food going rancid and destruction of nutrients by prolonged exposure to air
– helps you to better track how much your dog is eating
– helps bonding, particularly when combined with a bit of training and/or handfeeding
– helps your dog understand that you’re the provider of the food, not the floor
Did this happen in spite of proper socialization?
Yes, positive training and socialization should get him at least indifferent. At this point, I’d recommend doing that with professional guidance, though, where situations can be fully controlled to keep things below his threshold.