We argue that OmniGuide fibers, which guide light within a hollow core by concentric multilayer films having the property of omnidirectional reflection, have the potential to lift several physical limitations of silica fibers. We show how the strong confinement in OmniGuide fibers greatly suppresses the properties of the cladding materials: even if highly lossy and nonlinear materials are employed, both the intrinsic losses and nonlinearities of silica fibers can be surpassed by orders of magnitude. This feat, impossible to duplicate in an index-guided fiber with existing materials, would open up new regimes for long-distance propagation and dense wavelength-division multiplexing (DWDM). The OmniGuide-fiber modes bear a strong analogy to those of hollow metallic waveguides; from this analogy, we are able to derive several general scaling laws with core radius. Moreover, there is strong loss discrimination between guided modes, depending upon their degree of confinement in the hollow core: this allows large, ostensibly multi-mode cores to be used, with the lowest-loss TE01 mode propagating in an effectively single-mode fashion. Finally, because this TE01 mode is a cylindrically symmetrical ('azimuthally' polarized) singlet state, it is immune to polarization-mode dispersion (PMD), unlike the doubly-degenerate linearly-polarized modes in silica fibers that are vulnerable to birefringence.