Domain-generalizable speech emotion recognition (DG-SER) aims to ensure the robustness of SER models across unknown domains, which is essential for real-world human-machine interaction systems. Most DG-SER approaches employ alignment or adversarial strategies with domain labels to promote generalization. However, these strategies often confine generalization to predefined domains, limiting robustness under diverse real-world speech variations. To address these challenges, this paper proposes an emotion-preserving conditional information bottleneck framework (EP-CIB) for domain-free DG-SER. Specifically, EP-CIB introduces a nuisance proxy representation learning module to learn a nuisance proxy as the broad non-emotional variability without requiring any domain annotations, covering both defined and previously unseen domains. It then extracts coarse-grained emotion features via the consistency-aware emotion representation learning module. EP-CIB further introduces an emotion-preserving conditional information bottleneck that, conditioned on the emotion label, disentangles the nuisance proxy from the coarse-grained emotion representation, improving domain-free generalization under open-ended domain shifts. EP-CIB departs from implicit domain surrogates in prior domain-free methods by explicitly learning a proxy for nuisance domains and disentangling it from emotion features, enabling domain-free emotion representation learning. The state-of-the-art performance in both speaker-independent and cross-corpus settings, including an 18% improvement on EmoDB-to-CASIA transfer, demonstrates the effectiveness of EP-CIB for DG-SER.