DukeBen has done a great job explaining things from our point of view, so I'll address some of the later comments. Yes, the airlines from the southern side of the airport do sometimes call ready too early for 27, but so does the other one. How about calling ready for 34 from abeam D20 (tango/alpha intersection)? Seen that several times. And it's that airline in particular who complains about early ready calls.
A ready call indicates to us that you are ready for departure, and we will assess that accordingly in deciding the departure order. We are concerned with reducing the overall delays to departing aircraft, so you may not always depart in the order you think you should. For instance, in 16A/27D with a 16 departure to the northwest, it may be better to depart an aircraft off 27 who is not turning left, ie CORRS, SUNTI, ESDIG.
If we can get two aircraft away in a tight gap, one turning right and one turning left, again it is more beneficial to do this than send two on the same SID in quick succession.
If we can depart similar WT category aircraft, it may be beneficial to send the Heavy departure last, prior to a landing on the same or crossing runway to eat up the WT time. This way we are not twiddling our thumbs for two minutes with nobody moving. Or depart two Heavies or Supers out of order, again to minimise WT. These examples are, I believe in accordance with being first able to use the airspace.
You will appreciate that we mostly advise "going one out of sequence due....". We are not obliged to do this but it does save being asked "confirm you got my ready call" and then having to explain why you are not going when you think you should be, and wasting sometimes valuable r/t time.