Swift protocol initializer precludes adding more stored properties to struct - swift

Question

TL;DR:
I want a protocol to provide default init behavior, but the compiler resists adopters adding more stored properties. I solved this with composition instead of inheritance, but what's wrong with my original approach?
Motivation
I want to automate the transformation of objects from design specifications to runtime specs. I use the example of scaling a CGSize but the intent is more general than just geometric layout. (IOW e.g. my solution won't be to adopt/reject/rewrite autolayout.)
Code
You can paste this right into a Playground, and it will run correctly.
protocol Transformable {
var size : CGSize { get } // Will be set automatically;
static var DESIGN_SPEC : CGSize { get } // could be any type.
init(size: CGSize) // Extension will require this.
}
// A simple example of transforming.
func transform(_ s: CGSize) -> CGSize {
CGSize(width: s.width/2, height: s.height/2)
}
// Add some default behavior.
// Am I sinning to want to inherit implementation?
extension Transformable {
init() { self.init(size: transform(Self.DESIGN_SPEC)) }
// User gets instance with design already transformed. No muss, fuss.
}
// Adopt the protocol...
struct T : Transformable {
let size: CGSize
static let DESIGN_SPEC = CGSize(width: 10, height: 10)
}
// ...and use it.
let t = T()
t.size // We get (5,5) as expected.
But every Eden must have its snake. I want a Transformable with another property:
struct T2 : Transformable {
// As before.
let size: CGSize
static let DESIGN_SPEC = CGSize(width: 10, height: 10)
let i : Int // This causes all sorts of trouble.
}
Whaa? Type 'T2' does not conform to protocol 'Transformable'
We have lost the synthesized initializer that sets the size member.
So... we put it back:
struct T3 : Transformable {
// As before.
let size: CGSize
static let DESIGN_SPEC = CGSize(width: 10, height: 10)
let i : Int
init(size: CGSize) {
self.size = size
self.i = 0 // But this is a hard-coded value.
}
}
But now our new member is statically determined. So we try adding another initializer:
struct T4 : Transformable {
// As before.
let size: CGSize
static let DESIGN_SPEC = CGSize(width: 10, height: 10)
let i : Int
init(size: CGSize) { self.size = size ; self.i = 0 }
// Try setting 'i':
init(i: Int) {
self.init() // Get the design spec properly transformed.
self.i = i // 'let' property 'i' may not be initialized directly;
} // use "self.init(...)" or "self = ..." instead
}
Declaring i as var shuts the compiler up. But i is immutable, and I want i that way. Explain to me why what I want is so wrong... This page is too small to include all the variations I tried, but perhaps I have missed the simple answer.