Online continual learning (OCL) requires the models to learn from constant, endless streams of data. While significant efforts have been made in this field, most were focused on mitigating the \textit{catastrophic forgetting} issue to achieve better classification ability, at the cost of a much heavier training workload. They overlooked that in real-world scenarios, e.g., in high-speed data stream environments, data do not pause to accommodate slow models. In this paper, we emphasize that \textit{model throughput}-- defined as the maximum number of training samples that a model can process within a unit of time -- is equally important. It directly limits how much data a model can utilize and presents a challenging dilemma for current methods. With this understanding, we revisit key challenges in OCL from both empirical and theoretical perspectives, highlighting two critical issues beyond the well-documented catastrophic forgetting: (\romannumeral1) Model's ignorance: the single-pass nature of OCL challenges models to learn effective features within constrained training time and storage capacity, leading to a trade-off between effective learning and model throughput; (\romannumeral2) Model's myopia: the local learning nature of OCL on the current task leads the model to adopt overly simplified, task-specific features and \textit{excessively sparse classifier}, resulting in the gap between the optimal solution for the current task and the global objective. To tackle these issues, we propose the Non-sparse Classifier Evolution framework (NsCE) to facilitate effective global discriminative feature learning with minimal time cost. NsCE integrates non-sparse maximum separation regularization and targeted experience replay techniques with the help of pre-trained models, enabling rapid acquisition of new globally discriminative features. Extensive experiments demonstrate the substantial improvements of our framework in performance, throughput and real-world practicality.