I think the answer is a huge NO to that. Mirrors of Justice has Should Catholics be advocating for statehood for D.C.?
As mentioned in the comments the idea that the District would have it's own Reps and two U.S. Senators is just outrageous.
Still I think there has to be a balancing act there. Once we get past issues like abortion (which is important) D.C. has some problems with no easy remedy. Such as a good bit of the land in the District cannot be taxed!! So I am not saying subsidiarity ideas do not apply to D.C. but Statehood? Good grief no.