http://www.faa.gov/airports/resources/publications/orders/compliance_5190_6/media/5190_6b_appR.pdf
starting on p15
3. Purpose of Declared Distances:
a) To increase takeoff runway length at constrained airport sites while still
meeting design standards. (ex. increase runway takeoff length in one
direction while maintaining standard RSAs, ROFAs and RPZs.)
b) To enhance safety (improve RSAs, ROFAs, and RPZs) at constrained
airport sites. (ex. existing runway safety area does not meet standards,
but declared distances are used to effectively lengthen the runway
safety area beyond the stop end of the runway.)
....
e) Application of declared distance criteria may not be appropriate at
some GA airports, depending on the “design” aircraft (ARC). Pilots of
small GA aircraft do not have a requirement to use declared distances
to calculate allowable operating weights; therefore, use of declared
distances would not be appropriate at airports serving these aircraft
only. However, pilots of larger corporate or cargo aircraft do have a
requirement to use declared distances to calculate allowable operating
weights; therefore, declared distances would be appropriate at airports
serving these aircraft.
Dang...I bored....

Learn something new every day, or Friday night.
It's also discussed with respect to EMAS.
Looking at HPN, it has DDI, but the only real change from the airport diagram (on the plate) is the numerical value of the displaced threshold on 29. There is a "D" on the
big airport diagram.
There isn't an approach to 29. Maybe that is why it's not on the plate. I dunno.