I've never had the problem with an internal magazine rifle in over 50 years of shooting. When shooting at the range, I generally single-load. In the field, I work the action quickly after a shot, so if I were to miss, it's ready for another.
Another theory I have is that if the action is operated as quickly as possible after the shot, an animal wouldn't have time to recover it's accurate hearing from the sonic boom of the bullet going past. When one goes by, even at 200 yards, a .30-06 bullet sounds almost as loud as a .22lr fired 10 yards away. I've been in the 200 yard pull-target pit during a match and just 3 yards away, the loudness is amazing . I can imagine what it must sound like to the very sensitive ears of a deer at less than two feet.
Quicker is better; taking more than 3-4 seconds to jack in another shell can give your position away. The animal can recover it's wits and look around for movement.
Picher