The reason that there is extra benefit for those who have dependents (not just those who are married) is because of a couple of things. First, many jobs recognize married people need more in benefits, such as providing health care for families rather than just individual worker or housing for families (if that is a benefit of work, which it is even for some civilian jobs), and the military has to be competitive. Second, the Army did a study in the 90s that found that married soldiers were more stable, more responsible, and less likely to get into trouble or even get hurt than single sailors. This makes the cost of a married sailor worth the extra little bit, especially since from WW's example, neither of those two E-1s would likely be seeing any of their money for housing. Almost all commands have rules that force married E-1s through E-4s (at least) to live in military housing if at all possible. This means that all their BAH goes directly to housing. And the new rules require those living in housing to pay some of their electric bill, which means that the married E-1 would automatically have at least one extra utility bill, unlike the single E-1 living in barracks or (in certain areas) onbase single housing, that are like apartments, where he/she will not pay any utilities.
The studies show that they really don't do the same things all the time though. There is a marked difference in the performance levels of married soldiers compared to single soldiers because the married soldiers have someone else they are responsible for besides themselves. It may not always show through that way, but even in the civilian world, that is part of life. And the military is actually considering equalizing single and married BAH.