Well, + used to be the identify function before the introduction of complex numbers. Now + is the conjugate function (conjugate is equal to identity for reals).
I believe the identity function is useful when you have an operator where you want the passed-in function to do nothing. A somewhat contrived example would be an operator (let's call it ApplyPrint) that prints each element after applying it to the operator. You'd call it like so:
{1+⍵}ApplyPrint 10 20 30
11
21
31
If you don't want to apply the function, just call the identify function:
⊢ApplyPrint 10 20 30 'foo'
10
20
30
foo
Silly example perhaps, but illustrates its usefulness.
Regards,
Elias