Cannot quote you a source, but I believe there was a time when the up eye was favored because it was easier to snell. The straight and down eye were just later evolutions as materials, techniques, and preferences changed. In addition to the ones you mentioned, there are also jig eyes of various forms, loop eyes, flat-eyes, and 'no eye' hooks. Curious that what you say about saltwater hooks (conventional and fly), because almost all the ones that I'm familiar with are straight or down eye, except for the 'octopus' style hooks perhaps.

There are some that will argue that the different eyes have different hooking abilities, which explains why various styles have developed over the years. Manufacturers have tried different styles over the years to entice fisherman to buy different styles of hooks, and market differentiation resulted in the plethora of choices we enjoy today. If you are looking for a 'rational' reason for why there are all the hook styles there are, other than marketing, I think you are going to be disappointed.