Rivers are stock metaphors in Biblical eschatology. That has two sources of inspiration. One is the association of Edenic conditions with primeval rivers. The other is the fact that Palestine has little precipitation, so human life, animal life, and plant life depend on river water in that region.
It's interesting to compare and contrast the role of rivers in Christian symbolism and pagan symbolism. In both cases, rivers can represent a natural barrier between life and the afterlife. Paradoxically, rivers can stand for life and death alike.
If a river is sufficiently deep and wide, with a strong current, it will be impossible for a human to wade or swim across it. He will be swept downstream and drown. Rivers can also host animals that are dangerous to swimmers or waders, viz. crocodiles, anacondas, electric eels, bull sharks.
That creates a symbolic potential where someone can be stranded on the wrong side of the river. Maybe he can see the lush, idyllic landscape on the opposing river bank. That's a tantalizing view. Out of reach, but not out of sight.
In Greek mythology, the river Styx is the conduit to the netherworld. Because heathen Greeks had such a dismal view of the afterlife, the Styx is a river of death rather than a river of life. Because the the abode of the dead has fateful and forlorn connotations, it can't be a river of life, even though the dead continue to exist.
Contrast that with Christian symbolism about crossing Jordan into a land flowing with milk and honey. If we were to consistently elaborate the imagery, the river of life would be like a tidal river which is impassable at high tide, but passable at low tide. For a saint, death occurs a low tide. At that moment, the river ford is a dry bed.
Theoretically, the Garden of Eden might have been fluvial island. That would naturally segregate tame animals from wild animals. That would form a natural barrier between the idyllic sanctuary and the surrounding wilderness.