I studied beaver for many years, which led me to a formulation of a theory of cognition, namely that a complex instinct is an inherited body of expert knowledge. I ultimately wrote that theory up as a series of blog articles here: http://horsecognition.blogspot.com/ A warning: it runs about 30,000 words. Lots of critters are considered besides beaver, from horses to baby birds.
As for beaver, those I studied never had “feeding trails” nor did they forage. They built lots of dams in one place, using wood from a nearby aspen grove that they felled and cut into proper lengths. The paths were from the wood supply to the construction site. They eat the bark from their building materials so never have to forage. They also lay in an underwater food supply in the one pond that includes their house.
For example one pair built 36 small dams on a small stream. Another pair built 9 dams in a row on a large stream, each 6 feet high. This many-dam behavior obviously greatly increases the risk of predation so why do they do it? The standard answer was they cannot stop building, which is evolutionarily absurd.
My conjecture is they do it to drown the conifers which they cannot eat and which are replaced by fast growing aspen, their food supply. Mind you the ones that build the dams are not likely to be the ones that later eat the aspens, so they are tree farming for future generations. Nomadic tree farming for the good of the species, at great risk to themselves.
In fact if you fly over the boreal forest the only gaps in the conifer blanket are beaver ponds and meadows, including aspen groves.
I should add that beaver dams take a lot of wood. Our earth dams are just piles of compacted dirt, but a beaver dam is a lattice of wood pieces with an impervious mud face on the upstream side. Structurally it is a wood dam.
Backcountry horse riders are warned not to ride over old beaver dams because if a horses legs punch into that lattice it will be hell getting them out. It is very hard to dismantle.
The beaver could build just one dam with their house in the pond, then go out just for food as needed. Instead they build lots of dams which requires a great deal of time out of the water hence subject to predation. The difference in risk is enormous.