For the most part, it's simply more effective to do it edge-leading on a stone, and it'll also leave the apex stronger and more durable in doing so. The idea is to get the burr very thin and leaning to one side. Then fold it underneath the bevel in contact with the stone, so it can be neatly scrubbed off, leaving only a strong & stable apex behind. That can usually be done in just a very light edge-leading stroke or two per side on a stone.
If the steel is very ductile at all, edge-trailing will usually just draw out the burr further, making it broader and thinner (more flimsy) at the same time, and therefore more tedious to clean up. Burrs can eventually be reduced or removed this way if the touch is very, very light. But again, in doing so, it may tend to draw out the edge and make it too thin and too weak to be durable.