The hexagonal shape - with a wider breadth where the shoulders and torso of the corpse were placed - seems to be motivated by the shape of the human body in its natural burial position. We can see even in Ancient Egyptian sarcophagi, that when a person is placed lying down with his hands crossed around his chest, the sarcophagus naturally takes on a 'hexagonal' shape. Niklasson in 'Early prehistoric burials in Cyprus' notes that this arms-crossed position was common in most ancient civilisations, though there doesn't seem to be any conclusive reason for this besides that it may have represented an ancient Sun divinity. After Christianity spread, the X seems to have been adopted as a Christian symbol (Christopher Daniell, Death and Burial in Medieval England). In the Middle Ages, the arms at the sides position was also common, but Daniell admits that there isn't much insight as to what effect this had on coffins/burial customs.

The 'simple box shape' you speak of actually came into vogue in 19th Century America (Megan Springate, Coffins in 19th Century America). By exploring why the rectangular box became common, we can also find out why the hexagonal box was preferred in earlier times. Turns out the hexagonal shape was indeed considered 'anthropometrically shaped' (human body shaped), to the extent that it appeared to writer Nehemiah Adams as 'a seeming mockery of the rigid, swathed body'. Tharp also suggests that Americans of the time didn't view the rectangular box shape as 'simpler' than the hexagonal; in fact, the rectangle was a conscious design decision to minimise the coffin's resemblance to corpses: "Created a vocabulary that coincided with a promoted the 'beautiful death'." It was also around this century that caskets (rectangular 4 sided box) began to be distinguished from octagonal or hexagonal 'coffins'.

Summary: The classic coffin shape came from the sarcophagus, which was molded around the body with wood/papier mache and therefore matched the shape of a corpse. Current coffin trends are based on styles that emerged in the 19th Century, and are intended to either pay homage to tradition ('quintessential' shape) or create a pleasing aesthetic (rectangular) that does not connote a corpse.