Monolithic sponges combine low pressure losses and excellent heat transport properties and are consequently considered as promising catalyst carriers for fixed-bed reactors. Insights on how to design porosity and window size of monolithic sponges to resolve conflicting relations between low pressure losses, high thermal conductivities, and high space-time-yields (STY), i.e., a high catalyst inventory, are still unknown, especially at pilot or production scales. This study quantifies the outlined tradeoffs and assesses the potential of monolithic sponges as catalyst carriers compared to conventional packed beds of pellets. A state-of-the-art heterogeneous reactor model was applied in combination with a genetic multi-objective optimization algorithm to predict Pareto-optimal sets of sponge designs (max. STY, min. Delta p, Delta T-max <= Delta T-tol). As example, the methanation of CO2 was chosen. The Pareto-optimal set of sponge designs shows that small windows are necessary to obtain high space-time-yields comparable to the ones of conventional packed beds. As a consequence, the expected low pressure loss cannot be achieved. Because of excellent heat transport properties, which are weakly dependent on the throughput, monolithic sponges however allow stable operation under varying gas loads. The results demonstrate that monolithic sponges will probably not replace packed pellet beds of pellets for the steady-state production of chemicals. Instead, they provide a competitive option for small-scale, decentralized production for example within chemical energy storage and CO2 utilization.