There are a lot of good answers to #2 already, but most talk about abstract benefits and don't directly address the purely fiscal nature of the question. So he

There are a lot of good answers to #2 already, but most talk about abstract benefits and don't directly address the purely fiscal nature of the question. So here you go: There is no additional $40/day cost to the taxpayer. For a single servicemember living on base, the taxpayer is paying for their housing (the building may be paid for, but has limited capacity and ongoing repair & maintenance costs), their food, their water, their power, their garbage collection, their cable tv, and on and on. While it would be a pretty dull life, it is possible in some facilities to have all your needs met with essentially $0 living expenses (depending on availability of things like non-coin-op laundry machines). When a servicemember moves off base, for example to live with their spouse, all those become out of pocket expenses. The housing allowance is simply an offset to what otherwise would be a pretty drastic cut in total compensation.