Detecting TeV--PeV cosmic neutrinos provides crucial tests of neutrino physics and astrophysics. The statistics of IceCube and the larger proposed IceCube-Gen2 demand calculations of neutrino-nucleus interactions subdominant to deep-inelastic scattering, which is mediated by weak-boson couplings to nuclei. The largest such interactions are W-boson and trident production, which are mediated instead through photon couplings to nuclei. In a companion paper [1], we make the most comprehensive and precise calculations of those interactions at high energies. In this paper, we study their phenomenological consequences. We find that: (1) These interactions are dominated by the production of on-shell W-bosons, which carry most of the neutrino energy, (2) The cross section on water/iron can be as large as 7.5%/14% that of charged-current deep-inelastic scattering, much larger than the quoted uncertainty on the latter, (3) Attenuation in Earth is increased by as much as 15%, (4) W-boson production on nuclei exceeds that through the Glashow resonance on electrons by a factor of $simeq$ 20 for the best-fit IceCube spectrum, (5) The primary signals are showers that will significantly affect the detection rate in IceCube-Gen2; a small fraction of events give unique signatures that may be detected sooner.