No no no this is all wrong.
The root definition of “sandwich”, if it’s to mean anything at all, must be that it’s nominally hand-portable (even if it would require unrealistically large hands), and features wet foods symmetrically bracketed by single pieces of a dry food such as bread.
The main axes of disagreement are then:
nature of the sandwiching material: does it have to be bread?
disposition of materials: does the sandwiching material have to be repeatable prismatic “slices”, or can it be an object (such as a spherical bun) into which the filling has been inserted? The problem with the latter position being that it blurs the boundary with fully-encapsulated meals such as pirogies, pasties, pies etc.
Wraps and burritos and things like that are plainly not sandwiches. Because they have a similar bill of materials, they may be sold by sandwich places, who might include them under the heading “sandwiches” for operational purposes; and if you say “let’s get sandwiches for lunch” people might reasonably assume such foods as these to be included. But that’s just a kind of loose synecdoche, it’s not because anyone looks at a burrito and thinks “oh, a sandwich”.
As to the idea that the filling alone could disqualify something from being a sandwich, that’s just trolling and I shan’t dignify it with a response.