It wasn't always a "busy" street. Even today, I wouldn't call it "busy" like I'd call Westheimer busy. But for a little side street, it gets a lot of traffic from people detouring around the traffic at I-10 and the Beltway, going to the post office (which has a pretty brisk business), and shortcutting in general to get to the back of Bed, Bath & Beyond and Fuddrucker's and Pappasito's and all that other stuff that faces I-10 but has a rear entrance from that area.
My concern is that when City Centre is finally finished and there's a lot of traffic heading to and from the development, that street will become much busier than it already is and those brownstones literally dump you out right onto the curb of that street. There's a small sidewalk, but no room for anything like trees or any real buffer from the noise or constant traffic (think about the headlights shining in at night, etc). I wouldn't want to live there, is all.