Amorphous solid electrolytes often outperform their crystalline counterparts, but how disorder shapes ionic transport under strong electric fields is poorly understood. We use molecular dynamics with a machine-learned interatomic potential and a machine-learned Born-effective-charge model to measure Li mobility in amorphous Li₃PO₄ and in a crystal with Li vacancies, from the linear to the strongly nonlinear regime. The amorphous phase shows a much stronger field enhancement, and we trace this to a collective dipole effect. The migrating ion carries the same charge in both phases. Alone it would not make the amorphous phase respond more strongly. What makes the difference is the environment. In the amorphous network the surrounding atoms move with the hop. Their motion makes the work the field performs vary widely between hops. Since hopping rates grow exponentially with the work, the most strongly assisted hops can dominate the drift. Disorder thus enhances field-driven transport through the environment rather than the carrier itself, a mechanism that may operate in disordered ion conductors in general.