I never saw the attraction to using a bent knife, it feels awkward to me, all off center with no balance. But that's just me.
The entire point of the Kukri is its off centered balance. It has the balance that for most would resemble the feel of a hatchet or tomahawk but with the added benefit of being able to do knife and machete chores as well. Once you get used to a well made kukri it is awkward to be without one.
To answer the original question of "what are the advantages of a kukri over a large fixed blade knife," I would have to say that in such a one tool survival tool, the kukri can do it all well. After the initial learning curve the kukri is safe, efficient and a near perfect one tool choice. It can chop better than any other knife, especially over the long term. It can clear brush and process wood for virtually any task in a fraction of the time of a knife. It cuts like a knife, splits, stabs, hammers, digs and if ever needed as a self defense tool is second to none (as far as a blade is concerned.)
I normally take a variety of blades, Hawks or small axes when I camp and normally find that I use the kukri 80% of the time. I'm good with them, I enjoy using them and I can do things with a wrist flick that would take considerable effort with a standard knife. Don't get me wrong, I love my pocket knife, SRK, BK2, Trailmaster and KaBar but long gone are the days when they were my go-to blades.
If I were on that show and had only one tool to take with me, without a doubt it would be a kukri. It's not for everyone but I love them.