Parsers and delimited continuations[0] are monads, and there is manifestly no value there in some terms.
Monads allow us to reason about a computational environment "from the outside", as opposed to "from the inside"; functors and applicatives are restricted forms of the same thing. Functors allows us to reason about values in the computational environment. Pointed functors allow us to reason about pure values embedded in the computational environment, which we are going to demand remain unaffected by other operations. Applicatives allow us to reason about partially applied functions, or suspended computations (as opposed to mere values). Monads allow us to reason about nested computations (or sequenced, precisely in the sense that `a(b(c))` is both nested and sequenced).
My favorite monad: classical logic is just a monad in constructive/intuitionistic logic. That exemplifies the concept of computational environment, not burritos. It also shows that "there is no value in the box, only an opaque box and our imagination" can literally be the defining characteristic of a monad!
[0] For certain systems of continuation primitives.
[1] The "list monad" used in Haskell and elsewhere is actually the nondeterminism monad plus a bit of ordering on the side; the train visualization captures the less important of those two aspects. The nondeterminism monad can be extended to the discrete probability monad; that seems far more interesting.