Polly, I know what you mean. That's my idea for the Clematis database. Everything in alphabetical order under "Clematis," with no species names until you open the entry and learn the species. Of course, there are some species without cultivar names in both genera, but they get tucked away neatly at the end.
The reason that the rose section does this so neatly, however, is that virtually all of the roses in it are hybrids and therefore don't have a species to list.