I'm not sure I follow the terminology here. What does "if your counts are up" mean?
Why allow them to break contact and melt away (only to attack you another day)?
So proximity is an issue. One should strive to maintain contact and pursue the enemy killing as many as you can along the way. After all that is why you are there, yes?
The support and reserves should come from a QRF and be led by tenacious officers who will not just give up the chase so that the troops can return to base for a hot meal and a cold drink.
Why you should aggressively seek to maximise the kill rate per contact is to do what you should be doing anyway and that is to close with and destroy the enemy and secondly to prevent the enemy from building up their combat experience.
What could be mixed up a little is not whether to pursue the enemy but variations on how that pursuit would take place.
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