Defining functions `==` on a protocol or generically on a protocol does not quiet work. The difference between the 3 versions is in where `Equatable` is applied and how `==` is defined.

generic-inh-tree.swift

import Foundation
import XCPlayground

protocol Identifiable: Hashable {
    var id: String { get }
}

@objc class IdentifiableObject: NSObject, Identifiable {
    private let _id: String
    
    var id: String { return _id }
    
    override var hashValue: Int { return id.hashValue }
    
    init(id: String) {
        _id = id
        super.init()
    }
}

extension IdentifiableObject: Equatable { }

func ==<T: IdentifiableObject>(lhs: T, rhs: T) -> Bool {
    return lhs.id == rhs.id
}

// MODELS
class A: IdentifiableObject { }
class B: IdentifiableObject { }

let a = A(id: "equal")
let b = B(id: "equal")

func check<T: Identifiable>(lhs: T, rhs: T) -> Bool {
    return lhs == rhs
}

dump(a == b)           // <------------- FALSE
dump(check(a, b))      // <------------- TRUE

inh-tree-only.swift

import Foundation
import XCPlayground

protocol Identifiable: Hashable {
    var id: String { get }
}

@objc class IdentifiableObject: NSObject, Identifiable {
    private let _id: String
    
    var id: String { return _id }
    
    override var hashValue: Int { return id.hashValue }
    
    init(id: String) {
        _id = id
        super.init()
    }
}

extension IdentifiableObject: Equatable { }

func ==(lhs: IdentifiableObject, rhs: IdentifiableObject) -> Bool {
    return lhs.id == rhs.id
}

// MODELS
class A: IdentifiableObject { }
class B: IdentifiableObject { }

let a = A(id: "equal")
let b = B(id: "equal")

func check<T: Identifiable>(lhs: T, rhs: T) -> Bool {
    return lhs == rhs
}

dump(a == b)           // <------------- TRUE
dump(check(a, b))      // <------------- TRUE

proto-only.swift

import Foundation
import XCPlayground

protocol Identifiable: Hashable, Equatable {
    var id: String { get }
}

@objc class IdentifiableObject: NSObject, Identifiable {
    private let _id: String
    
    var id: String { return _id }
    
    override var hashValue: Int { return id.hashValue }
    
    init(id: String) {
        _id = id
        super.init()
    }
}

func ==<T: Identifiable>(lhs: T, rhs: T) -> Bool {
    return lhs.id == rhs.id
}

// MODELS
class A: IdentifiableObject { }
class B: IdentifiableObject { }

let a = A(id: "equal")
let b = B(id: "equal")

func check<T: Identifiable>(lhs: T, rhs: T) -> Bool {
    return lhs == rhs
}

dump(a == b)           // <------------- FALSE
dump(check(a, b))      // <------------- TRUE