We have had some close calls cutting timber too. Dad once got whacked by a fairly small tree in the shoulder, and was out of commission for a few days. Grandpa very nearly got killed when I was in high school- dad was cutting a 250 year old white oak in the pasture, and a sudden gust of wind pushed the tree the wrong direction. Grandpa tried running, but he was running straight away in the same direction the tree was falling. About 20 or 30 feet up, the trunk forked into two huge limbs, each a couple feet in diameter. The two limbs fell just on either side of grandpa, with him in the middle!

The ground literally shook when that tree fell. If it hadn't been for his guardian angel that day, grandpa would have been planted six feet under like a fence post on the spot! ('course, he wouldn't listen when dad told him to stay back, either.) Dad's best friend was killed almost 20 years ago while trying to push a fallen tree off the edge of his field with a bulldozer. He didn't realize the roots were still in the ground, and the more he pushed, the trunk just built up tension like the limb of a giant crossbow. The tree slipped over the bucket and hit him in the head. Just a couple weeks ago, a local guy got instantly killed when the trunk split, and hit him in the chest.
Eh. Sorry for getting so morbid there.
Back on topic, I haven't seen the bend of a kuk's blade as all that great of an asset while chopping fallen wood. I mean, after all, most fallen wood is laying on the ground. If I try using the sweet spot on the kuk's belly, the tip would hit the ground. The only real option is to chop with the tip, except my kuk simply cannot cut effectively with the tip, and any attempts to do so result in numb fingers from the shock within just a couple swings.