Right now everything on this site is organized by Linnean binomials for a few reasons. First, the systematic names are how I usually think about things, so I know them and don't have to sit around looking things up all the time. Second, a lot of species have multiple common names, or no common name, or different common names in different places, etc. Similarly, a single common name can be used for multiple species. So in organizing things according to common names, you either have to do a lot of cross-listing and leave out some species, or make up some names for nameless taxa and arbitrarily choose one of the common names to use. Both approaches are problematic. Furthermore, common names rarely say much about the relationships between plants, so they are generally either uninformative or misinformative when it comes to trying to understand how plants are related.
That said, coming up with alternative common name listings for things is somewhere on my list of things to do, but not very high on the list and a time-consuming enough task I don't know if it'll happen.