I can only address his concerns baised upon my own use of the double in Texas, Montana, Idaho, Canada, Alaska, and Zimbabwe.

I have taken game from squirrel to elephants.

Range:
I can shoot and hit with an iron sighted double as well as I can with an iron sighted bolt rifle.

With a scope sighted double I have taken game to a little over 300 yards.

With a scoped bolt rifle in a Magnum calibre I have taken game farther... But I have not hunted with a scope Magnum double.

Reloading.
I have discovered that the immediate second shot has proven to be much more useful to me than a bolt rifle with 3 or more rounds in the magazine.

And I do not just mean for DG at point blank range, but for general hunting as well.

Reliability.
Nothing beats the reliability of a double rifle.

Expense
By their design double rifles are a LOT more expensive than most bolt rifles.
However when you compare them to custom bolt rifles the difference narrows.

For me, I have found a double rifle to be FAR superior to ANY other rifle action type for MOST hunting.

I never set out to prove this "theory", I just "discovered" it to be true after using a double rifle for most of my hunting here in North America preparing for Africa.