1D is indeed not good one for radial operator. But on higher dimensions, e.g. 3, one need to think of inner product with $r^2$ weight function, so it cancels the the boundary term. Of course this gives another term when doing integration by parts, and that is why $d/dr$ alone if not enough for hermiticity.
Of course this corresponds also to the fact that "plane wave" in radial coordinate has some function of $r$ in the denominator, because of energy conservation, e.g. $e^{ikr}/r$ in 3D.
