1 recurves are pretty and can have great flowing lines.
2 Recurves are particularly good at certain types of cutting tasks.
3 Recurves are a particularly useful characteristic on a fighter.
#1 is pretty obvious.
Some recurve porn

Someone mentioned Hossom. He does production blades for Spyderco but the Chainsaw is what I think they are based on.
#2 takes some explaining , but compare a kukuri with a katana. To make a good cut with a katana you have to pull back as you hit to make the weapon slice.
A kukuri does that for with the shape of the blade. It is at an angle so it bites into the target at a single point along the edge putting all the force of the blow in a tiny places which it then widens. A straight edge would hit along the length of the blade making the surface area many times larger than if it hit at a single point.
If you want to try this out for cheap i highly recommend the Cold Steel kukuri machete ,the regular size one. It is cheap and if you hit the sweet spot on the blade you can take down a thick hardwood branch in one swing. It is very impressive for such a light blade.
The forward weight of a recurve can also be useful but it needs to be bigger kukuri style on.
#3 is why I love recurves. The same physical advantage as above along with bigger wound channels and a real advantage with snap cuts etc.
Check out how similar 2 fighters ,a fixed and folder are.
Here is a more subtle recurve in the CR SEAL knife which I think makes it a much better looking and balanced package than the GB.
I don't mind the sharpening at all but I use a Lansky. So long as you use one of the newer systems there is no problem.