The magnitude of the light source is not dependent on distance and I never wrote it was.
Of course it is - the observed magnitude is. The further you are from a light source, the dimmer it appears.
Shine a torch right in your eyes and it's uncomfortably bright. Observer it from 50 yards and it's much dimmer and smaller.
So if we can't see Polaris from the southern "hemisphere" because it's too far away then we should observe a gradual dimming of it as you get further away to the point where it can't be seen any more. That isn't what is observed at all. It just gets lower in the sky - again, a degree lower for each degree of latitude - until we can't see it any more because it is "under" the horizon.
The absolute magnitude of Polaris varies and is not dependent on the observer.
Apparent magnitude, of which you write, is a different measure altogether.
And your claim that Polaris simply becomes lower and lower for each degree of latitude is true, but there is more.
There is always the issue of atmoplanar effects and terrestrial objects that will eventually interfere with the ability to see any object.
But, really I find all of this quite rich!
Here, AATW writes:
A bright object will appear dimmer and smaller until you can't see it.
Does his happen with Polaris? No.
But here, he flips the script and starts arguing with...himself:
Of course it is - the observed magnitude is. The further you are from a light source, the dimmer it appears.
Shine a torch right in your eyes and it's uncomfortably bright. Observer it from 50 yards and it's much dimmer and smaller.
So, which position are you arguing again?