Well, some of the swords do 'morph' in shape at times in the series. ForceEdge, Rebellion do, according to their function. Yamato apparently didn't, but it shows that the shapes are not static. They might yet be a reflection of sorts of their wielders, though clearly Vergil is not a mini-Sparda, he wasn't driven by the same things Sparda was, and Yamato did not change at all to reflect that.
I assume Sparda didn't make all of those swords but acquired them from the Underworld, as there are many demonic weapons floating around that were not in his possession; and so Yamato just enabled a different style to a broadsword, and that he used various kinds of swords over time. Not sure why Dante and Vergil ended up with their respective blades, but they suit their personalities... if we're going to talk 'what if', they might simply have chosen the swords they thought looked the coolest.