The married ones get BAH because while you're in your hotel room, servicemen/women must be given the BAH so their spouses and children maintain a place to live, or provided separate government quarters AKA base housing. Did you REALLY need that additional $2500 to supplement your VERY generous travel claim? Did you really NEED to receive quarters in a hotel AND double dip to get BAH? You were provided adequate quarters. And you have not checked into your first PERMANENT duty station, so how could you have rent or mortgage in a place you haven't moved to yet?
Just like mentioned earlier, Single DLA is not authorized for your first duty station. That's Army, Navy, Air Force, officer, enlisted, surgeon, grunt, etc. It is a FEDERAL regulation.
Quit crying. You will learn very soon that you will have more money being single than your married counterparts, despite them receiving slightly higher pay. Your post did not start out as a simple query, you asked a question then began whining how it wasn't fair. So yes, naturally it's going to rub some the wrong way. Had you just asked the question, you would not have received such responses. Your overall point that moving requires the same hardship and expense, married or not is false. It is more difficult and more expensive with a family.
You're in the military now, dude. Suck it up, do your job, follow the rules and you'll be fine. Otherwise you're going to have a difficult time while you're in.