The downside is that you would have to put () (Rust's version of “nil”) in a bunch of functions to fulfil the requirements of the callback's signature since otherwise the type inferred from the function would be the value of the last expression

Wouldn't co/contra-variance solve this entirely? It works just fine in Scala for example

    scala> def runTwice(f: () => Unit) = {
         |  f()
         |  f()
         | }
    runTwice: (f: () => Unit)Unit

    scala> runTwice{ () =>
         |  println("moo")
         |  1
         | }
    moo
    moo

Note how it expects a function that returns Unit, i'm passing in a function that returns an Int (1), but the compiler is perfectly happy.