For beams, is it beneficial/recommended from structural integrity standpoint to have longitudinal reinforcement placed at the corners of the stirrups or not really needed?
1- A member subjected to given loading is treated as a space truss formed by a series of joined planar trusses.
2- The concrete member reinforced with longitudinal and transverse reinforcement resists shear/torsion by producing a circulatory shear flow at the outermost part of the beam cross-section. Thats why using steel rebars are preferred at circumferential surface of beam (with a nominal cover of 25-50mm.
3- Also the concept of concrete confinement is will suited/played if steel truss is distributed at circumferential surface of beam.
Confined and confined unconfined concrete terminology, benefits shown in attached curves.
Also using longitudinal reinforcement is needed in almost every concrete structure.
It's easier to detail the bars in the corner, since dimensioning is unnecesary. It has a small advantage in confinement also.
The only reason I can think of to not detail the longitudinal bars in the corner of the tie/stirrup, is if the designer is concerned about the bars not being all the way to the bottom of the tie or stirrup, due to the bend radius of the ties/stirrups. I think if that's going to make the beam fail, the designer should just add or upsize the longitudinal reinforcing.
I was referring to confinement of the concrete - having the bars farther out puts a little more concrete inside the bars. The difference would be minimal, and the necessity probably non-existent, in most cases.
Placing longitudinal bars in the corners of beam stirrups is an ACI 318 code requirement to ensure (near) instantaneous tension development of the stirrups. See ACI 318-08 Section 12.13.2. (I don't have my ACI 318-19 handy with me, but I don't think it's changed.)