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Connected technologies have engendered a paradigm shift in mobility systems by enabling digital platforms to coordinate large sets of vehicles in real time. Recent research has investigated how a small number of connected vehicles may be coordinated to reduce total system cost. However, platforms may coordinate vehicles to optimize a fleet-wide objective which is neither user nor system optimal. We study the behavior of optimized fleets in mixed traffic and find that, at small penetrations, fleets may worsen system cost relative to user equilibrium, and provide a concrete example of this paradox. Past a critical penetration level, however, optimized fleets reduce system cost in the network, up to achieving system optimal traffic flow, without need for an external subsidy. We introduce two novel notions of fleet-optimal mixed equilibria: critical fleet size for user equilibrium (CFS-UE) and critical fleet size for system optimum (CFS-SO). We demonstrate on the Sioux Falls and Pittsburgh networks that 33% and 83% of vehicles, respectively, must participate in the fleet to achieve system optimum. In Pittsburgh, we find that, although fleets permeate the network, they accumulate on highways and major arterials; the majority of origin-destination pairs are either occupied exclusively by users or by the fleet. Critical fleet size offers regulators greater insight into where fleet and system interests align, transportation planners a novel metric to evaluate road improvements, and fleet coordinators a better understanding of their efforts to optimize their fleet. History: This paper has been accepted for the Transportation Science Special Issue on Emerging Topics in Transportation Science and Logistics. Funding: This work was supported by the U.S. Department of Transportation [Mobility21] and the National Science Foundation [CMMI-1931827]. Supplemental Material: The online appendices are available at https://doi.org/10.1287/trsc.2022.1189 .