Current climate policies and national pledges are insufficient to achieve the necessary reduction in CO2 emissions, underscoring the urgency of carbon dioxide removal (CDR) from the atmosphere. Direct air capture (DAC) is an engineered CDR process with substantial removal potential but also one with clear technical limits and opportunities for enhancement. One such improvement is the optimization of the material, enabling the separation. To investigate this from a quantitative perspective, this study evaluates DAC performance when replacing existing sorbents with theoretical ones designed to optimize the process. In order to do so, the adsorption isotherm parameters of CO2 for different isotherm models were optimized along with process design variables to minimize energy and maximize productivity. Combining equilibrium and rate-based models, our analysis offers insights from thermodynamic, reactor, and economic perspectives. The results show that optimal sorbents have the potential to significantly improve the DAC performance obtained with existing sorbents, for example, Lewatit VP-OC-1065 and MIL-101, especially in terms of energy consumption and costs. This requires that some critical sorbent characteristics are met: moderate cost (e.g., <30$/kg), long lifetime (e.g., >2 years), and a linear driving force in line with other gas separation processes (e.g., k(LDF) > 0.001 s(-1)). Furthermore, our findings highlight that optimizing productivity and energy consumption enables the identification of minimum-cost configurations for DAC. This work underscores the importance of tailored sorbent design in advancing DAC toward cost-effective, efficient CO2 removal solutions.