This was explained to me last year by a gate agent friend and this is my recollection of her comments.
She said that she makes the call depending on how full the flight is. They will assign seat to standby passengers (in order of priority i.e. revenue standby, student standby, employee standby, etc ) as soon the know the flight is wide open and the possibility of running out of seats is almost nil.
When the flights are full, they start to assign the standby's in order of priority within the 15 minute prior to departure (i.e. if you haven't checked in for the flight there is a good chance you will lose your seat). She said ticket agents don't like to start pulling people from the back on operational upgrades for a couple of reasons, they are probably already on the plane, they may be sitting with somebody with a different locator and that can start a domino effect of the seat shuffle, may cause additional delays trying to sort out seating etc.
She said that you have a better chance of getting an operational upgrade in this situation by not having a seat assigned to you - you will be part of the masses, but will obviously have higher priority. She warned me this method is a
LONG shot for the operational upgrades and you will probably end up with a middle seat - in the back OR worse in a denied boarding situation (i.e. all the revenue passengers have a seats and even though you are a revenue passenger with a booking on the flight you can't get on because
ALL of the seats are taken by other revenue passengers. In other words its really really
REALLY important to get to the gate with a seat assignment.
With regards to the operational upgrades she said that when they know the plane if oversold by revenue passengers and they have to start the juggling process early with REVENUE passengers that's when they will go through the passenger list to move the SE, E and P's up front.
The other problem I was told was they don't like to bump Rev passengers up front is because there may not be enough meals (please hold the comments on the quality of the meals or whether or not you even care about the meal back

). You can usually guess the standbys in J because they either have a Y meal or no meal.
In summary it is simplest for the gate agent NOT to move people around, but simply to fill the empty seats the standbys.