But they are difficult to sharpen

The plastic sharpening block does leave something to be desired, but I've found other rod-shaped objects that work well. I now have a small lathe and I may end up turning rods specifically for this purpose.

(they) lift a lot of grain when used in the wrong direction

The simple solution to this is to use the smallest radius to test the grain, then move to a larger radius once you've determined the optimum direction.

(they) don't fit as far into a corner as a router bit.

I guess that depends on the size of the bit you're using, but regardless, I haven't found it to be a problem. I try to radius parts before installing them if possible, but even when radiusing after the fact, I've found that any corner that the tool won't get into is also going to be inaccessible to my hands and feet, or to the kayak skin, which is the main reason I radius parts in the first place.

On the plus side, I can reach into places where a router simply won't fit.

They aren't a perfect solution, but they're well worth having.