There are ubiquitous distribution shifts in the real world. However, deep neural networks (DNNs) are easily biased towards the training set, which causes severe performance degradation when they receive out-of-distribution data. Many methods are studied to train models that generalize under various distribution shifts in the literature of domain generalization (DG). However, the recent DomainBed and WILDS benchmarks challenged the effectiveness of these methods. Aiming at the problems in the existing research, we propose a new domain generalization task for handwritten Chinese character recognition (HCCR) to enrich the application scenarios of DG method research. We evaluate eighteen DG methods on the proposed PaHCC (Printed and Handwritten Chinese Characters) dataset and show that the performance of existing methods on this dataset is still unsatisfactory. Besides, under a designed dynamic DG setting, we reveal more properties of DG methods and argue that only the leave-one-domain-out protocol is unreliable. We advocate that researchers in the DG community refer to dynamic performance of methods for more comprehensive and reliable evaluation. Our dataset and evaluations bring new perspectives to the community for more substantial progress. We will make our dataset public with the article published to facilitate the study of domain generalization.