Actually your two equivalents are not so equivalent, although in most contexts they would imply the same thing.
There is an interesting file in the root directory.
This is an existential statement that asserts the existence of an entity that can be described as "interesting file in the root directory".
An interesting file is in the root directory.
This does not really have the same connotation, but instead asserts first the existence of an instance of an "interesting file", via the indefinite article "An", and then asserts something more about that entity, namely that it is "in the root directory".
You may still think there is no difference. If so, consider the following possible wider contexts:
There is an interesting file in the root directory of each computer in this network.
An interesting file is in the root directory of every computer in this network.
The first means that each computer has an interesting file, possibly different for different computers. The second means that there is a single interesting file that is on every computer.
There lives an amazing fish in my pond.
An amazing fish lives in my pond.
Similarly your fish-pond example has the same fine distinctions that show up only in certain contexts.
So I am trying to figure out, is there some grammatical basis for usage of the expression "there + verb"?
Well there is a grammatical basis, as shown above by the fine distinctions between such constructions and the apparently equivalent ones without the "there". This also explains why all bare existential statements of the form "There is [a[n]] X." cannot be rephrased except as "[A[n]] X exists.". Some other usages include:
There comes a truck loaded with stones.
A truck comes, loaded with stones.
There flew in a dozen birds through the window.
A dozen birds flew in through the window.
There stood a lone pillar in the courtyard.
A lone pillar stood in the courtyard.
There arose a dispute about money.
A dispute arose about money.
In most cases, it is of the form "There V X [A]." where V is an intransitive verb (no object), X is a noun phrase that is the subject of V, and A is an optional adverbial phrase that modifies X if possible or V otherwise.