This sounds exactly like the kind of equipment you would want overhead in a major combat operation. Both visual and communications intelligence along with the means to detect missiles and possibly defend itself are all capabilities you want during major combat operations.
Why have a drill over a major American City if they aren't trying to spy on Americans? Major cities have a large quantity of communications systems all over the spectrum. Police, Fire, Ambulance, Taxi, and even Amateur radio operate in the ranges of interest. They will be able to receive both local and distant broadcast stations that will change based on position and atmospheric conditions. This is simply an exercise in how to operate the equipment to find and decode various communications. Add a ground component with training signals intentionally generated by the military and this becomes more realistic.
As for privacy concerns, this is very valid and you should remember that no telecommunications network can be completely secure. It is also important to note that any communications intercepts of civilian communications will be concerned with capabilities, not content.