If you have seperated date/time dimensions, the number of possible cells in the multidimensional space that need storing individually will be the same, since the conceptual space is the cross product of the dimensions. To give another example: Say I have a table of products with 8 things in it, a table of 100 customers, and 5 stores. A cube storing the sums may keep 4,000 distinct entries. If two of the dimensions are merged to form a hierarchy, since perhaps, each customer has a relationship 1:1 with a store, then you'd end up with a Customer (by store) dimension of cardinality 500. This gives, likewise, a dimensional space with up to 5000 (correction - 4000) cells.
Hey. Why stop there! If separate date/time dimensions leads to the same number of possible cells in the resultant cube space as the a single date/time dimension, that same logic should apply to everything. If sound logic, then that principle should be true. Then why separate customer/product/store dimensions? An equally sound dimensional design would be to have a single fact table related to one dimension with a composite key of product/customer/store and the hierarchies built from that key.
I hope we both agree that that design is NOT sound. Why that design is not sound is the same reasoning that the composite date/time dimension is not sound (Again, read chapter 2 of The Data Warehouse Toolkit for lengthy justification why it's not.) Because a Time member, i.e. 12:01 AM is not uniquely related to only one member of the date dimension. It's related to every member of the date dimension and the same justification to separate Product and Customer and Store is the same logic applied to separate date and time. A date is a date and a time is a time and they are not the same.
I'm done. No mas.