High capacity polymer dielectrics that operate with high efficiencies under harsh electrification conditions are essential components for advanced electronics and power systems. It is, however, fundamentally challenging to design polymer dielectrics that can reliably withstand demanding temperatures and electric fields, which necessitate the balance of key electronic, electrical and thermal parameters. Herein, we demonstrate that polysulfates, synthesized by sulfur(VI) fluoride exchange (SuFEx) catalysis, another near-perfect click chemistry reaction, serve as high-performing dielectric polymers that overcome such bottlenecks. Free-standing polysulfate thin films from convenient solution processes exhibit superior insulating properties and dielectric stability at elevated temperatures, which are further enhanced when ultrathin (~5 nm) oxide coatings are deposited by atomic layer deposition. The corresponding electrostatic film capacitors display high breakdown strength (>700 MV m^-1) and discharged energy density of 8.64 J cm^-3 at 150 °C, outperforming state-of-the-art free-standing capacitor films based on commercial and synthetic dielectric polymers and nanocomposites.