Double Dispatch Obsolete?

Since I started with OO I've been told switching on typeid is a big
no-no. E.g.

void Washer::wash( Vehicle myVehicle )
{
  if( typeid(myVehicle) == typeid(Car) )
   Washer::washCar( myVehicle );
  else if( typeid(myVehicle) == typeid(Bike)
   Washer::washBike( myVehicle );
  else if( typeid(myVehicle) == typeid(Boat)
   Washer::washBoat( myVehicle );
}

The alternative is the more correct Double Dispatch. E.g.

void Washer::wash( Vehicle myVehicle )
{
  myVehicle.washer( this )
}

void Car::washer( Washer w )
{
  w.washCar( this );
}

Now, consider we change Washer to XMLConverter and wash() to write().
This will still work, but when we want to go backwards and read XML and
write a Vehicle we need to switch on some kind of type id label anyway. E.g.

Vehicle XMLConverter::readVehicle( XMLdoc doc )
{
  Vehicle v;
  string s = doc.readAttr();
  if( s == "Car" )
   v = new Car();
  else if( s == "Bike" )
   v = new Bike();
  else if( s == "Boat" )
   v = new Boat();

  return v;
}

So why not just give every MyObject a typeName() method and switch or
std::map<char*, fncPtr> on that throughout all dispatchers?

//Daniel