Class-incremental learning (CIL) is commonly evaluated under predefined schedules with fixed or nearly equal class increments, leaving irregular class-arrival scenarios underexplored. However, practical CIL systems may need to update whenever new categories emerge, without forcing them into balanced task partitions. We formalize this setting as Free-Flow Class-Incremental Learning (FFCIL), where the number of newly arriving classes can vary substantially across learning stages. We show that variable class arrivals alter the class composition of incremental training, the reliability of new-class classifier statistics, and the consistency of representations learned across increments, causing clear performance degradation in both conventional and pre-trained model (PTM)-based CIL methods. To improve robustness under FFCIL, we introduce a general framework consisting of Class-Wise Mean (CWM), which replaces instance-wise loss aggregation with class-wise averaging; Dynamic Intervention Weight Alignment (DIWA), which adjusts new-class weight calibration according to the current increment size; and Head-Agnostic Alignment (HA), which performs feature-level correction for PTM-based methods using current and previous-class feature supervision. Extensive experiments across diverse methods, datasets, and class-arrival schedules demonstrate the general impact of FFCIL and the consistent effectiveness of our framework.

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