The (#) operator is quite natural and useful in the diagrams library, but the thing is that even though it is *implemented* as function application, it is *semantically* not a function application. It only serves to furnish shapes and diagrams with additional properties; it's type is very restricted, so to speak.

Since the use cases mentioned (diagrams, lenses) are very similar, perhaps there is a general combinator (&) that does the job for both, but which has a much more restricted type and is not equivalent to reverse function application. Maybe an abstraction like "Settable functors", "Thingomorphisms with properties" or something like that.

In lens and in diagrams the type signature really does have to be a -> (a -> b) -> b, because the type of the underlying object could (and often is) changed. A critical part of lens is support for changing field types:

>>> ("Hello","Heinrich") & over both length

(5, 8)

there it goes from (String,String) -> (Int,Int). There isn't any usable commonality between the input and output type. Similarly in diagrams you can use it to change it between R2 to R3, or otherwise enrich the target in ways that change its type.