If an owner has purchased a P &P Bond on the GC, is it appropriate for the GC to procure P&P bonds for the subs?

I have hired a GC and we are currently negotiating a lump sum price for the project. The owner plans on procuring a Payment and Performance bond on the GC but the GC is also including the cost for procuring P&P bonds for each of the subs (to protect themselves) and then wants to pass this cost along to the Owner. Should the Owner be paying for P&P bonds for both the GC and the subs?