enum conformance to RawRepresentable

"although I feel that conformance should be synthesized by the compiler"

Yes, here your rawValue is of type String, not Int. Simply create your enum like:

enum WeekDay: String {
    case monday, tuesday, wednesday, thursday, friday
}

And then create a WeekDay like this:

let monday: WeekDay? = WeekDay(rawValue: "monday")
let notADay: WeekDay? = WeekDay(rawValue: "foo")

Of course you can also add a custom init which takes an integer as argument:

enum WeekDay: String {
    case monday, tuesday, wednesday, thursday, friday
    init?(integer: Int){
        switch integer {
        case 0 : self = .monday
        case 1 : self = .tuesday
        case 2 : self = .wednesday
        case 3 : self = .thursday
        case 4 : self = .friday
        default : return nil
        }
    }
}

And create your weekDay like:

let monday: WeekDay? = WeekDay(integer: 0)
let notADay: WeekDay? = WeekDay(integer: 30)

Apparently your definition of init?(rawValue: Int) prevents the compiler from inferring the RawValue type automatically. Adding a type alias helps:

enum WeekDay: String {
    typealias RawValue = String

    case monday, tuesday, wednesday, thursday, friday

    init?(rawValue: Int){
        switch rawValue {
        case 0 : self = .monday
        case 1 : self = .tuesday
        case 2 : self = .wednesday
        case 3 : self = .thursday
        case 4 : self = .friday
        default : return nil
        }
    }
}

Alternatively define your custom init function with a different parameter name:

enum WeekDay: String {

    case monday, tuesday, wednesday, thursday, friday

    init?(rawInt: Int){
        switch rawInt {
        case 0 : self = .monday
        case 1 : self = .tuesday
        case 2 : self = .wednesday
        case 3 : self = .thursday
        case 4 : self = .friday
        default : return nil
        }
    }
}

As of Swift 5 there is no error of having a second init?(rawValue: Int) in addition to synthesized init?(rawValue: String). But if you want to override that RawRepresantable implementation and have rawValue be Int, it is possible.

extension WeekDay : RawRepresentable {
    
    typealias RawValue = Int
    init?(rawValue: Int){
        switch rawValue {
        case 0 : self = .monday
        case 1 : self = .tuesday
        case 2 : self = .wednesday
        case 3 : self = .thursday
        case 4 : self = .friday
        default : return nil
        }
    }
    
    var rawValue: Int {
        switch self {
        case .monday : return 0
        case .tuesday :  return 1
        case .wednesday : return 2
        case .thursday : return 3
        case .friday : return 4
        }
    }
}
print(WeekDay.init(rawValue: 2)) // Optional(WeekDay.wednesday)
print(WeekDay.RawValue.self) // Int