Excellent idea. Two additional reasons: (1) many parents would want veto power on what kids spent their time on and are exposed to, including video games; and (2) you could suggest quietly buying the game through the parents, to avoid complicating the kids' relationship with getting stuff.

Some other, more expensive, activities (e.g., tennis lessons together, when the family of one of the BFFs isn't affluent) are harder for more people to do this, but video games are relatively inexpensive.