Mid-course corrections don't include this data. Most missiles is going to select target on its own.
Proper two-way datalinked a2a missiles like Meteor are still an exception, not a rule. For SAMs it depends, but assuring what independent seeker will home on what you want and not on anything else is a very major problem even now.
//that's assuming datalink isn't jammed//
Early to mid course, the BVR missile has yet to select a target, as the homing system is yet to be activated. You want to bring the missile as close to the target as possible before opening up the homing system. That would give the target the least amount of time to react and with it the highest potential percentage of kill. Remember the target's RWR is going to look for the missile's CW illumination, and this waveform is easily distinguished from pulse frequency that search radars use. If the missile goes autonomous early with its homing illumination, the target gets warned early by the RWR and can take appropriate actions.
Midcourse corrections is guiding the missile to the spot where it can be best go terminal and homing. Even if the missile itself has not selected the target, the fire control radar on the fighter already did and is trying to bring the missile close enough to the intended target before lighting the seeker.
