The answer is that NO coaster *needs* shoulder restraints (excepting Stand-Up and Flying Dutchman models, and a case could be made for not having them on the stand-ups...).
The shoulder bar as we now know it was invented in 1975 and is credited to Thomas Milton Humphries. The patent is #4,005,877. Its first use was on the Corkscrew roller coaster at Knott's Berry Farm; I would be interested to see if there is any earlier use of a shoulder bar on an amusement ride. There is not, to the best of my knowledge.
Earlier ride designers, most notably Lee Eyerly, demonstrated that an inverted rider is effectively secured by a lap restraint, and nobody has yet demonstrated to me convincingly that a shoulder bar is any more effective. In fact, I have seen some particularly frightening demonstrations that shoulder bars are in fact neither appropriate nor adequate for effectively securing riders. This tells me that the benefit of the shoulder bar is primarily that it *looks* more effective than other means.
Arrow Development (and by extension Arrow-Huss and Arrow Dynamics) have adopted the shoulder bar for use on their multi-element looping coasters. Iron Dragon has shoulder bars because Arrow's suspended coaster tub uses essentially the same seat molds as the multi-element looping coaster...a seat design which is already optimized to accommodate shoulder bars instead of lap bars. In fact, Iron Dragon could probably run safely with no active restraints at all.
--Dave Althoff, Jr.