Birdman was not gimmicky with the "1 take" aesthetic in any way. I believe that it did push the story to be better too. The narrative centered around a Broadway play where you only have one chance to get something right, just like one takes. Everything has to fall right in place. There's isn't a cut or redo on stage. Riggan was striving for perfection and that's what Inarritu managed to pull off with Birdman, a seemingly flawless film.
*Deleted a second posting*