1. Which plants can be rooted only with hormone?
2. Which plants cannot be rooted, even with hormone?
There is excellent general information on plant propagation in The Brooklyn Botanic Garden Gardener’s Desk Reference (Janet Marinelli, editor; Henry Holt, 1998), which explains which plants are most successfully propagated by seed, by division, by layering, by leaf or hardwood or softwood or stem cuttings, and by root cuttings.
There really is no resource that will provide a comprehensive list of plants that can or cannot successfully be propagated from root cuttings, but a member of the faculty here who specializes in propagation says that the key element that determines whether a plant can be propagated in that way is age. Each plant has different abilities, and some are easily rooted, such as Salix (willow), while others, like Quercus (oak), or Arbutus (madrona), are very hard to root, especially as they mature. As far as use of rooting hormone, it can help the process, and it will prevent rotting, but if you are a strictly organic gardener, you should be aware that it is a chemical substance.