Why can't I assign a *Struct to an *Interface?

When you have a struct implementing an interface, a pointer to that struct implements automatically that interface too. That's why you never have *SomeInterface in the prototype of functions, as this wouldn't add anything to SomeInterface, and you don't need such a type in variable declaration (see this related question).

An interface value isn't the value of the concrete struct (as it has a variable size, this wouldn't be possible), but it's a kind of pointer (to be more precise a pointer to the struct and a pointer to the type). Russ Cox describes it exactly here :

Interface values are represented as a two-word pair giving a pointer to information about the type stored in the interface and a pointer to the associated data.

This is why Interface, and not *Interface is the correct type to hold a pointer to a struct implementing Interface.

So you must simply use

var pi Interface

This is perhaps what you meant:

package main

type Interface interface{}

type Struct struct{}

func main() {
        var ps *Struct
        var pi *Interface
        pi = new(Interface)
        *pi = ps

        _, _ = pi, ps
}

Compiles OK. See also here.