The back-action damping of mechanical motion by electromagnetic radiation is typically overwhelmed by internal loss channels unless demanding experimental ingredients such as superconducting resonators, high-quality optical cavities, or large magnetic fields are employed. Here we demonstrate the first room temperature, cavity-free, all-electric device where back-action damping exceeds internal loss, enabled by a mechanically compliant parallel-plate capacitor with a nanoscale plate separation and an aspect ratio exceeding 1,000. The device has 4 orders of magnitude lower insertion loss than a comparable commercial quartz crystal and achieves a position imprecision rivaling optical interferometers. With the help of a back-action isolation scheme, we observe radiative cooling of mechanical motion by a remote cryogenic load. This work provides a technologically accessible route to high-precision sensing, transduction, and signal processing.