The primary function of Type I alveolar cells is to provide a large, thin surface area for gas exchange. They form the alveolar-capillary barrier along with the capillary endothelial cells and the basement membrane. This barrier is crucial for facilitating the diffusion of oxygen and carbon dioxide between the alveoli and the blood. Additionally, these cells help maintain the integrity of the alveolar space by preventing fluid leakage into the alveoli.