The standard description of cavity-modified molecular reactions typically involves a single (resonant) mode, while in reality, the quantum cavity supports a range of photon modes. Here, we demonstrate that as more photon modes are accounted for, physicochemical phenomena can dramatically change, as illustrated by the cavity-induced suppression of the important and ubiquitous process of proton-coupled electron-transfer. Using a multi-trajectory Ehrenfest treatment for the photon-modes, we find that self-polarization effects become essential, and we introduce the concept of self-polarization-modified Born-Oppenheimer surfaces as a new construct to analyze dynamics. As the number of cavity photon modes increases, the increasing deviation of these surfaces from the cavity-free Born-Oppenheimer surfaces, together with the interplay between photon emission and absorption inside the widening bands of these surfaces, leads to enhanced suppression. The present findings are general and will have implications for the description and control of cavity-driven physical processes of molecules, nanostructures, and solids embedded in cavities.