Alloy composition homogeneity plays an important role in the device performance of III-V heterostructures. In this work, we study the spatial composition uniformity of n-InGaAs/i-InGaAs/p-GaAs core-shell nanopillars monolithically grown on silicon. Cross sections extracted along the axial and radial directions are examined with transmission electron microscopy and energy-dispersive X-ray spectroscopy. Interestingly, indium-deficient segments with width ~5 nm are observed to develop along the radial 1120 directions in the InGaAs layers. We attribute this spontaneous ordering to capillarity effect and difference in group-III adatom diffusion lengths. The slight fluctuation in indium content (~4%), however, does not induce any noticeable misfit defects in the pure wurtzite-phased crystal. In contrast, the heterostructure exhibits excellent alloy composition uniformity along the axial [0001] direction. Furthermore, abrupt transitions of gallium and indium are seen at the heterointerfaces. These remarkable properties give rise to extraordinary optical performances. Lasing is achieved in the core-shell nanopillars upon optical pump despite the observed alloy composition fluctuation in the radial directions. The results here reveal the potential of the InGaAs-based core-shell heterostructures as efficient optoelectronic devices and high-speed heterojunction transistors directly integrated on silicon.