Improving composite cathode function is key to the success of the solid-state battery. Maximizing attainable cathode capacity and retention requires integrating suitable polymeric binders that retain a sufficiently high ionic conductivity and long-term chemo-mechanical stability of the cathode active material-solid-electrolyte-carbon mixture. Herein, we report block copolymer networks composed of lithium borate polycarbonates and poly(ethylene oxide) that improved the capacity (200 mAh g<sup>-1</sup> at 1.75 mA cm<sup>-2</sup>) and capacity retention (94 % over 300 cycles) of all-solid-state composite cathodes with nickel-rich LiNi<sub>0.8</sub>Co<sub>0.1</sub>Mn<sub>0.1</sub>O<sub>2</sub> cathode active material, Li<sub>6</sub>PS<sub>5</sub>Cl solid electrolyte, and carbon. Tetrahedral B(OR)<sub>2</sub>(OH)<sub>2</sub> <sup>-</sup> anions immobilized on the polycarbonate segments provide hydrogen-bonding chain crosslinking and selective Li-counterion conductivity, parameterized by Li-ion transference numbers close to unity (t<sub>Li+</sub>~0.94). With 90 wt % polycarbonate content and a flexible low glass transition temperature backbone, the single-ion conductors achieved high Li-ion conductivities of 0.2 mS cm<sup>-1</sup> at 30 °C. The work should inform future binder design for improving the processability of cathode composites towards commercializing solid-state batteries, and allow use in other cell configurations, such as lithium-sulphur cathode designs.