in my opinion character can either come from nature, which is the character that you are referring to, but it can also come from the bowyer. One of my favorite bows to look at is Pearlies "two of two" bow.
http://www.primitivearcher.com/smf/index.php/topic,37380.0.htmlI love this bow, it has a ton of character: curves, tips, skins, etc. all of which were imparted by the bowyer. it looks like this bow came from a pretty "boring" stave, but is now a far cry from boring.
I do like the look of a natural character bow, i like making them, i actually think they are easier to make since there is usually little to no correction needed if you are leaving them as is, and i am not yet familiar with the techniques that are required to impart my own character such as extreme curves and fancy tips.
Oh and even though i have a lot of nice osage, HHB, and hickory staves i still build some board bows now and then, that still doesn't make me a wus...only fiberglass does that!