Well, I'm happy it works for you that way, and I'm certainly not an expert on the matter, but from the limited experience I've had, I don't think it's necessary at all to withdraw food to have a good relationship with your bird.
All birds I've had wanted to be with me because they wanted my attention, not food. The little one I have now will do anything just to get close to me. He doesn't even want the food, sometimes I'll offer him some and instead of grabbing it, he climbs on my hand.
This is a personal belief, but I don't want my animals to want to be with me because I give them food.