III-V nanowire (NW) heterostructures are promising candidates for advanced silicon-integrated optoelectronics and quantum light sources. The interfacial abruptness in axial NW heterostructures grown by the vapor-liquid-solid (VLS) method suffers from the reservoir effect in a catalyst droplet. The interfaces of NW heterostructures based on group V interchange are commonly expected to be sharper due to low concentrations of highly volatile group V atoms in a droplet. Here, we present a self-consistent growth model of VLS III-V NW heterostructures based on group V interchange, influenced by desorption of group V atoms, and show that sharp interfaces are not guaranteed in the general case. The model provides explicitly the interfacial profiles across double NW heterostructure of any composition. The obtained solution contains only one parameter describing different transport of A and B atoms through liquid. The interfacial abruptness depends critically on a binary or ternary NW from which it starts, as well as on the stationary composition of the second segment. We analyze the available experimental data and explain why the interfacial profiles in GaAsxP1-x/GaAs/GaAsxP1-x NWs are much sharper than in GaP/GaAsxP1-x/GaP NWs. The effect originates from a slower transport of As atoms in any catalyst as compared to P atoms. As a result, feeding and removing As atoms in the GaP-to-GaAsxP1-x transitions is much slower than for P atoms in the GaAs-to-GaAsxP1-x transitions with similar x. Our approach should be useful for tuning the composition and sharpening the interfaces of any III-V NW heterostrutures based on group V interchange, and provides a basis for further advancements in this field.