Type III tape has been used in both main and reserve construction for many years. One of the earliest uses was the military MT-1X canopies (both main and reserve). The early Tempo reserves also used Type III for line attachment loops. In fact, when the Aerodyne Smart Reserve was first shown at the PIA Symposium in Jacksonville in 2003, it also had Type III tapes. Obviously all of these canopies could meet the stringent drop test requirements with this tape.
Virtually all sport main canopies use Type III including some canopies that had a history of hard openings (early PD Sabres).
Type III use has been proven over the years. But Skydiving has evolved from 120 mph freefall speeds to speed skydiving at speeds reaching 300 mph.
Stronger canopies typically lead to bulkier canopies. Ten years ago the demand was for smaller packing canopies. Today, with higher freefall speeds, strength rules over pack volume so even newer construction techniques, as well as materials are seen. If you examine the newest reserves (Precision r-Max), you will find that attachment tape material is woven spectra and it is no longer bartacked to the lowersurface, but integrated into the loadbearing rib structure.