Easier to hit a deer where you want if it's not moving.
I totally understand the argument about an alert deer though. I've not ever had one jump the string because of my stopping it though. And if he happens to be chasing a doe, you've got to do something to stop that bad boy. In fact, I'm going to by a whistle for just such occasions. They are so "1 track minded" when they are chasing, it's dern near impossible to stop them.