I would agree with your reason number one. I would just tweak it slightly. I think that the parents who give nice gifts (based on what they can afford) are (in general) people for whom the chinuch of their children in a main focus of their lives. Children who have parents who are so dedicated to them, on average, live up to their parents goals more closely.
P.S. I very specifically wrote the words “on average”. I am very well aware of many cases where good, dedicated parents have children who stray far from their parents ideals. But I believe it to be indisputable that children do better with dedicated parents.
P.P.S. On behalf of myself and many other Rabbeim, I would like to express my appreciation to to all those of you who open your wallets and checkbooks to so generously give the gifts that you can afford (whatever amount they may be). I would like to doubly thank those of you who include a note or card of appreciation that specifically mentions some of the nice attributes of the Rebbe and how your child has gained from him. Children do not often express genuine appreciation for all of the dedication and hard work that the Rabbeim put it. It is easy to feel that your efforts are not noticed and not making a real difference. Reading a card that says “My son is excited to learn parsha because of the excitement with which you tell it over” or the like, can make a Rebbe’s day.