Bally Heck,
We do that (but surely you should be able to fly the SID without local knowledge)!! but it doesn't work on a heavy aircraft at max RTOW. Get the noise charts out , measure the radius of turns and check it against the groundspeed at Take Off Flaps. You will make it on 737 & 757 using heading select and take off flap, but the radius of turn increases by the square of the speed so the faster you go the "greater*greater" the radius. I don't think that it is surprising the Virgin and PIA go outside the MNR, I would have thought that a 747 to Lahore or Karachi is a heavy (fast) aircraft.
If you are really keen get a copy of the Pan Ops regulations (they are in the Jepp. Text Manual) and read the regulations. They are a mile away from what was drawn 25 years ago by the MIA.