The primary purpose of integer surrogate keys is increased performance, thus we even use them in Type-1 Slowly Changing Dimensions, where changes to dimension attributes are not important, and hence, overwritten during update.
Star schemas work even with natural keys only, so feel free to streamline the design as much as you desire.
However, another reason to use surrogate keys has to do with the impossibility of guaranteeing that the source system will *always* provide a unique natural key. For example, consider acquisitions and the consequent merger of systems or simply the migration to new transaction system.
In your example, it is probably not significant, since it is unlikely that there are very many business systems on this planet using non-standard calendars. However, remember that there are other calendars, such as fiscal and religious calendars.
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The reasonable man adapts himself to the world. The unreasonable one persists in trying to adapt the world to himself. Therefore all progress depends on the unreasonable man. - George Bernard Shaw