Personally I like the general concept of the scout rifle, but I find that people do stick to Jeff Cooper's finalized specs of the scout rifle much to strictly. If people stick to Jeff Coopper's more early thinking on the concept -light, handy, fast-handling, relatively powerful, capable of engaging man-sized targets at common ranges, then the scout rifle concept is a much better one in my opinion. Boomer's note about a shorty M-1A is a fine example of a rifle that fits this bill very well, and yet many would automatically disregard this rifle because it's a semi-automatic, and it's a tad over Jeff Cooper's cap on weight limits. The truth is such a rifle hits all Jeff Cooper's original target areas of a scout rifle.
And let's not forget that Jeff Cooper was just a man with one man's opinion, just like the rest of us. He did not invent the concept of a light, handy rifle, meant for all around use. He is generally credited with refining the concept and giving it a name, but I think Jeff Cooper himself was more of a pragmatist than a theorist and he would likely have agreed that sticking to inflexible definitions set out by anyone, even himself, is a bit of a silly notion, and not useful in the least.
Going back to the OP. What is the advantage of a scout rifle?
In my opinion, compared to may of today's specialized firearms, it's a practical rifle that's easy to carry, easy to bring to bear quickly, easy to fire in most any position, easy to hit common targets with at common ranges, and powerful enough to reliably deliver one-shot kills on whatever you're pointing it at.