A precise, scalable, and computationally efficient mathematical framework is proposed for region-wide autonomous electric vehicle (AEV) fleet management, sizing and infrastructure planning for urban ride-hailing services. A comprehensive techno-economic analysis in New York City is conducted not only to calculate the societal costs but also to quantify the environmental and health benefits resulting from reduced emissions. The results reveal that strategic fleet management can reduce fleet size and unnecessary cruising mileage by up to 40% and 70%, respectively. This alleviates traffic congestion, saves travel time, and further reduces fleet sizes. Besides, neither large-battery-size AEVs nor high-power charging infrastructure is necessary to achieve efficient service. This effectively alleviates financial and operational burdens on fleet operators and power systems. Moreover, the reduced travel time and emissions resulting from efficient fleet autonomy create an economic value that exceeds the total capital investment and operational costs of fleet services.