Can't speak for others, but I do, solely out of necessity. I want to make my own, it's just that none of the hickories on my property are a problem, so I just let them continue to grow. There's a good bit of Ash, though, so I might try to save a straight log and cut stock with a chainsaw. I would buy hickory lumber, but the thickest I can find is 4/4, and it ain't cheap. 4/4 is probably enough to make it work, but I would rather have a little bit extra as margin for error, so 5/4 is what I'm looking for...
As to the limbwood, it might work, but the grain circumference is going to be very small compared to the a wider log, and it will be virtually impossible to get a piece with straight grain orientation for a striking handle. I could be wrong, that's just my take on it.
100% sapwood is ideal, but I remember reading somewhere that the U.S. Forest Service states in their service manuals that up to 50% heartwood is acceptable if not satisfactory, so long as the grain orientation is <45°; closer to 90° is ideal.