I started with a little cheap red fiberglass bow, graduated to as bear compound, then discovered osage self bows. I leave peopel there freedom to use compounds but to me compounds are as fun as dancing witha fat woman, their clumsy and not very graceful.
Even though the simple wood bow or a sexy asian static recurve bow may not launch arrows with as flat a trajectory as a so called compound bow, there is just something that feels light and right about a more primitive bow. I might add that for most of us a primitive bow costs almost nothing but time and effort. The poorest man in the world could probably come up with a highly effective hunting implement with the natural materials at his disposal.
To me hunting with a compound only proves that one has the money to buy one, if proving something is important to someone.
Back to the point of the post, I don't think there is any real historical conection between the Eastern composite horn bows and the modern compound bow. One might be able to make the case of a connection in physics principles. Both kinds of bows try to achieve a sort of let off of stack on the pull by leverage. One uses a gear ratio method by means of pulleys, the other uses a lever principle like adding a pipe to a wrench handle to give more turning power.
Other than those similarities the two bows are as different as night and day when compared in construction, use, and methodology.