"If a jeweler can "facet" a diamond, why cant I sharpen one?" You can and do "facet" your diamond, just like a jeweler does. He doesn't make points 'cause he doesn't need them, nor do I. When needed, I just loosen the shank and rotate it. The previous facet becomes an edge, to the wheel.
Saves needless diminishment of the expensive diamond and the wheel doesn't really want to be stuck, so no point needed, it wants to be shaved. Moving points produce spiral grooves on spinning surfaces, not a surface I prefer on my grinding wheels.
You do orient your diamond to the inclination that produces what become vertical edges when rotated, right? I ask because only a straight up, (wrong) orientation of a diamond dressing point, would "flatten" the "point", requiring wasting diamond surface to rectify.
Bob