I'll be the forum heretic on this one - I think the button should be marked 'BUTCH', not 'SPORT', as the only advantage I can see on a manual is to help a slow driver pretend they are going fast.
By the time grip is beginning to go, there is quite enough force in the steering and increasing the kick-back is no benefit. Sport mode doesn't seem to provide any more feedback, it just requires more force.
And while people describe the throttle behaviour with butch words like 'toughen' and 'sharpen', all it seems to do is open the throttle more for a given amount of pedal movement - so that there is less throttle sensitivity when grip is low, which is no improvement at all.
I reckon the button is there to make a 30mph trip to the supermarket feel quicker than the actual little-old-lady pace.
In an automatic, being able to alter the shift programme seems a real benefit, though I thought the autos were adaptive, so won't they make the same change on their own after a few miles?