Why do nonclustered Indexes use clustered indexes instead of the table data pages directly?
The clustered index IS the table. In the classic phone book analogy where everything is ordered by Lastname, Firstname there's not some other book that the phone book refers to.  The Phone book IS the book, and it's in that order.

When you have a clustered index, it contains all the data for all the columns in the table, ordered by the key you pick.

In the absence of a CI, the non-clustered indexes need to refer to something so they refer to the RID (row identifier) which is a surrogate key the engine assigns.