3) We do have some well-deserved amenities. Your service member has earned the use of the amenities for the entire family with their service. Living on base can make it easier to utilize them.
Military installations offer a lot. Shopping at the commissary just makes more sense when you live ¼ of a mile away, you can attend a worship service at the chapel, and even scout out the clinic parking lot on your way home from the gym to see if you think the pharmacy will have a ridiculous wait that day. Every branch has services/programs specifically for the military family, including things like classes on resume writing, playgroups for small children, volunteer opportunities and sports for all ages.
Living on base might mean you can actually walk to many of these places. During the school year our current installation is filled with families and children walking to school. We can walk to the chapel, several parks and even the commissary from our house. If you are a family with only one car, that can be a huge selling point.
I also feel more informed when I live on base. To get home I have to actually pass all of those signs that tell me what is going on that week. I am reminded of different activities by my neighbors or when I see folks at the different facilities on base. I need a million reminders to make sure I attend that awesome free concert on base.