Than, PY, your neglecting the Human element of this management tool.
Hunters, whether they be allowed to hunt with rifles, or forced to hunt with slug guns will shoot the first deer they see, more often than not.

Second, many of todays slug guns are accurate to 150+ yards with todays modern slug\propellent combinations. So your again losing your mangament tool.

My rifle allows me to kill any deer that i see, which is legal to shoot. It doesn't force me to kill those deer. That is a choice that I must make (the human element).
It gives me a greater freedom, as well as a greater level of responsibility.
Do I trust myself to make that 250-300+ yard shot?
My rifle (Ruger, 7mm) will shoot that range and well beyond, with superb accuracy in the right hands.
I don't practice at those ranges, and don't believe that I have any business taking shots at those ranges. Again, I'm not forced to take long shots, I hunt in fairly dense cover, but do have opportunities for shot longer than 150 yrds.

Why restrict a hunter to making shots less than that? If they are comfortable making those shots. many hunters even with slugs will try longer shots than that. The reality is that slugs while accurate to 150+ yrds, lack the punch to cleanly kill deer much past that.
My rifle does not lack the punch to make a clean ethical kill at those "extended" ranges.

Slug guns are not a management tool, as you think. They are in many cases a safety element, for high population center, lowly forested regions. Those reasons for their requirements I agree with.
Not as a wildlife population tool, to increase deer numbers and antler size.