BAH should be the same rate regardless of dependents or not. They need to get rid of family seps pay also or give it to everyone. Call it what you want or make it a part of the base pay and then give COLA dependent on location it is treated as pay by military members. Same pay, for the same rank, for the same years of service. The military has specialty pay such as flight pay, nuke pay, doctor pay (which can vary greatly on specialty), bonuses (dept head, nuke, etc). None of these are mysteries and can total a pretty good chunk of change in many cases.
BAH is alot better than it used to be. I never had Marines living in poverty. BAH at all my duty stations was plenty to let them live reasonably. More than anything most my Marines who couldn't find affordable housing, had unreal expectations for their rank or couldn't balance a check book. I have seen ghost marriages. More than ghost marriages, I saw Marines separate from their spouses and never get divorced for 2,5,10 years later because it just was easier and they got more money. More pay for the service member and Tri Care for the spouse. The most popular of them all is young first term Marines getting married way too young to a stranger just to "get off base." I almost couldn't blame them because of the extra crap they make the single Marines do. 4-6 hour field days, extra watch, Gunny or 1stSgt in their stuff, limit to a 6 pack of beer, going home on deployment first. I always felt bad for the single Marines and as one of the very few single officers I always tried to advocate for fairness of my single Marines. But that is another debate for another day.