Probably worth noting that fish, even predatory ones, don't necessarily have binocular vision, and vice versa for herbivores. Sperm whales are the largest living predators and lack it; fruit bats, who don't hunt, do have it.

There ARE incentives to develop it, or retain it, based on those lifestyle differences, but it makes for a somewhat fuzzy heuristic.

The other thing is this is pretty much restricted to fish and their mutant descendants, the tetrapods. Get outside the chordates and you find different solutions to these problems. Arthropods have several distinct kinds of eye architecture and sometimes their strategies generalize well: house flies (which are prey and scavengers) and dragonflies (which hunt) both have similarly-structure eyes; if anything I think the dragonfly has wider coverage. Spiders often rely on widely-placed eyes of differing strengths and ranges; mantis shrimp only have the two eyes, on stalks, and are renowned predators.

So it might look like a generalizable rule because it applies to so many of the most obvious, easy-to-examine large animals you can find, but remember they're our close anatomical cousins, and they're solving the problem with very similar design constraints.

(Also, primates -- many primates who spend a lot of time in trees, but don't hunt, have binocular vision. In their case it's there because of its benefits for rangefinding and spacial awareness in an arboreal environment.)