Because otherwise you cannot annotate it with a type AdditionFunction. You need to put this value, which is of type int -> int -> int, and the way the F # syntax works is that you have no way to do this using the let-bound style.
Your options:
let f : int -> int -> int =
fun a b -> ...
let f a : int -> int =
fun b -> ...
let f a b : int =
...
and only the first has a type that you could replace with an alias.
. int -> int -> int, , AdditionFunction.
- . , , .