On circular orbit burning prograde/retrograde makes the orbit elliptical with raising or lowering the orbit on the opposite side of the body, making the burn position the new periapsis/apoapsis respectively.
Now, burning radial or antiradial makes the orbit an ellipse as well, but by changing simultaneously the apoapsis and periapsis. In some cases the new shape of the orbit may be desirable (e.g. setting up a bielliptical transfer). In other (in reverse) it could help circularize an elliptical orbit to a given altitude if its periapsis and apoapsis are on two sides of that altitude.
Yet I almost never read about this being done. The bielliptical transfer is described as pure prograde/retrograde burns.
Is there a specific reason? Is it considerably less efficient than a combination of prograde/retrograde burns setting up the same orbit, or something like that?