My children are small yet but I moved every year as a child. FOR ME...I found that when they made a big deal out of it, I did. Until one year they told me about 2 weeks before hand, and asked my new teacher to schedule something special to make me feel more wlecome. She actually had all the kids in the class stand up and introduce themselves and make up a sentence saying why they thought it was a good idea to have a new in the class and why it was good for me and what thier favorite thing to do was. That helped get conversations started. Not all teachers are willing to do that but it also depends when this transition happens. For some kids that might be a bad idea. If he is very shy and withdrawn a bit then it may be easier for him to find a "buddy" maybe the new teacher could someone in the class that is also interested in the same things and put them next to each other.
But in a nut shell, I think you are right. If he is not getting all he can and a challenge from this school then why waste the money? Have you spoken with his teacher or the principal? Sometimes they don't see that the children need something specific. But if you are hearing the same things from other parents there then change it. In the long run he will thank you for it! I feel that I am a well rounded, friendly, outgoing person because of all the moves. I make friends easily too. Mind you this took time to grow but the ends justify the means. Good luck!