I do remember looking into them before and translating them into Haskell and they ended up not being identical to functions in the trivial sense that you suggest, but I forget how.
For instance if we have (map inc [1 2]), there exists a transducer function T such that:
(reduce T [1 2]) == (map inc [1 2])
Okay?
Now, the clever thing is this: why don't we allow map to be called without the list argument? Just let it be called like this:
(map inc)
;; if it were partial application, then:
((map inc) [1 2]) ;; same as (map inc [1 2])
(reduce (map inc) [1 2]) ;; same as (map inc [1 2])
It's like a linear operator; like LaPlace. Composition of entire list operations in the regular domain corresponds to composition of operations on individual elements in the "t-domain".
This is wrong. You've missed the point.
(map inc [1 2])
(reduce ((map inc) conj) [] [1 2])
(sequence (map inc) [1 2])
Transducers are mostly function and function composition, but with a specific signature. There are a handful of contracts on a transducer, so it is useful to have a name, so you can say "this function takes a transducer" and "this function returns a transducer".
They also work well in cases where you don't know if/when a new value is coming, like in channels or observables. This is because they aren't necessarily wed to the seq abstraction from the get-go.