The purpose of the date dimension is not just for showing the date value.
The main purpose is about summarizing the data.
Data available at the date level can be rolled up by periods, by weeks, by quarters, by years.
Date hierarchy is typically implemented with the rollup dimensions.
These roll up dimension tables can be used for holding the foreign key from the aggregated facts.
The definition of Gregorian calendar is consistent and common. Typically the ETL process for populating the gregorian calendar does not need to use data from the OLTP source system.