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-1 at 1.75 mA cm-2) and capacity retention (94 % over 300 cycles) of all-solid-state composite cathodes with nickel-rich LiNi0.8Co0.1Mn0.1O2 cathode active material, Li6PS5Cl solid electrolyte, and carbon. Tetrahedral B(OR)2(OH)2 - 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 (tLi+~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-1 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.