Why is DTA recommending non-clustered indexes that match the clustered Primary Key index?
The index does not match exactly what already exists.  The Clustered index (the primary key) contains all the other data related to the table.  But the nonclustered index (NCI) contains just the primary key. The resulting NCI is much narrower than the clustered index.

Having a non-clustered index on just the primary key has a few benefits that may be relevant here.  But, I also want to caution you to take the DTA and the suggested missing indexes with a grain of salt.

Benefits of having a non-clustered index in addition to the clustered index (on the same key).


Foreign Key Check Constraints - If other tables use this one as a
foreign key reference, then having a narrow NCI will speed this up
dramatically. 
COUNT or EXISTS - If you frequently check for the existence of this
value (or count them) without any other conditions, then having an
NCI will also be beneficial.  Having a narrower index to use for
these is extremely efficient, especially if the base table is very
wide.


Basically, even though both would be seek operations, if the NCI can be used it will typically be very narrow and can fit more ID values per page on disk so will reduce memory grants.