Solid-state batteries based on lithium metal anodes, solid electrolytes, and composite cathodes constitute a promising battery concept for achieving high energy density. Charge carrier transport within the cells is governed by solid-solid contacts, emphasizing the importance of well-designed interfaces. A key parameter for enhancing the interfacial contacts among electrode active materials and electrolytes comprises externally applied pressure onto the cell stack, particularly in the case of ceramic electrolytes. Reports exploring the impact of external pressure on polymer-based cells are, however, scarce due to overall better wetting behavior. In this work, the consequences of externally applied pressure in view of key performance indicators, including cell longevity, rate capability, and limiting current density in single-layer pouch-type NMC622||Li cells, are evaluated employing cross-linked poly(ethylene oxide), xPEO, and cross-linked cyclodextrin grafted poly(caprolactone), xGCD-PCL. Notably, externally applied pressure substantially changes the cell's electrochemical cycling performance, strongly depending on the mechanical properties of the considered polymers. Higher external pressure potentially enhances electrode-electrolyte interfaces, thereby boosting the rate capability of pouch-type cells, despite the fact that the cell longevity may be reduced upon plastic deformation of the polymer electrolytes when passing beyond intrinsic thresholds of compressive stress. For the softer xGCD-PCL membrane, cycling of cells is only feasible in the absence of external pressure, whereas in the case of xPEO, a trade-off between enhanced rate capability and minimal membrane deformation is achieved at cell pressures of ≤0.43 MPa, which is considerably lower and more practical compared to cells employing ceramic electrolytes with ≥5 MPa external pressure.