The large variety of hybrid carbon nanotube systems synthesized to date (e.g., by encapsulation, wrapping, or stacking) has provided a body of interactions with which to modify the host nanotubes to produce new functionalities and control their behavior. Each, however, has limitations: hybridization can strongly degrade desirable nanotube properties; noncovalent interactions with molecular systems are generally weak; and interlayer interactions in layered nanotubes are strongly dependent upon the precise stacking sequence. Here we show that the electrostatic/polarization interaction provides a generic route to designing unprecedented, sizable and highly modulated (1 eV range), noncovalent on-tube potentials via encapsulation of inorganic partially ionic phases where charge anisotropy is maximized. Focusing on silver iodide (AgI) nanowires inside single-walled carbon nanotubes, we exploit the polymorphism of AgI, which creates a variety of different charge distributions and, consequently, interactions of varying strength and symmetry. Combined ab initio calculations, high-resolution transmission electron microscopy, and scanning tunneling microscopy and spectroscopy are used to demonstrate symmetry breaking of the nanotube wave functions and novel electronic superstructure formation, which we then correlate with the modulated, noncovalent electrostatic/polarization potentials from the AgI filling. These on-tube potentials are markedly stronger than those due to other noncovalent interactions known in carbon nanotube systems and lead to significant redistribution of the wave function around the nanotube, with implications for conceptually new single-nanotube electronic devices and molecular assembly. Principles derived can translate more broadly to relating graphene systems, for designing/controlling potentials and superstructures.