TLDR: Is there a general rule saying that you can split rational Bézier curves, in such a way that both segments have end points where w=1?
For quadratic rational Bézier curves it seems true, that you can split them in two, and have unity end weights. My reasoning here is as follows: quadratic rational Bézier curves with unity end weights are conic segments. A segment of a conic segment is sill a conic segment, therefore a segment of a quadratic rational Bézier curve with unity end weights is another quadratic rational Bézier curve with unity end weights.
Sidenote: Is there a quadratic rational Bézier curve that isn't a conic? I think not, but I got that part from intuition, so please correct my if I assumed this falsely.
For higher order rational Bézier curves it would be nice if the same applied.
I would accept a straight answer to the question, if someone could also point to an algorithm to determine the control points and weights of the segment curves, if they exist, that would be appreciated as well.
@bubba: Please don't be mad at me for asking about rational Bézier again, I promise that I mostly switched to non-rational, and you are correct in pointing out that it simplifies a lot.