I suppose that argument could work, if the nature of the child's disease was explained. However, it wasn't. The scenes with the family were perfunctory handled, and I felt that they were a plot device.
For myself, I see another revenge film. I have to ask myself, is Star Trek capable of doing a film where revenge is not a theme? I know that revenge doesn't need much explanation, which is why it works well across the cultural and language barrier. Still, there must be other themes that do equally well.
(The issue with drone strikes I think has less to do with its methodology, and more with its impact which I think gets lost. One of the concerns with warfare is how a civilian population responds to being attacked. Studies have shown that a civilian population will become more galvanized against an attacker after an attack which results in the deaths of non-combatants. Our drone strikes aren't precise - wedding parties and children are being killed. These strikes are influencing how people in those regions view the American military, and, by extension, the American government. If ST: ID was about the impact of drone strikes, I think it would be useful for the script writers to have placed Khan in a populated area, where the possibility of killing civilians would be a factor in whether or not one should launch an attack. [Why is Star Trek not using drones for combat? Is there a policy in Starfleet which forbids the use of drones?])