While broadcast may not be specifically in the text, Channels' site does specifically call out antenna and cable feeds as the primary source of content, which TVE sources are offered to augment that:
Similarly, the Channels Plus page makes no mention about adding your own outside content, nor working with any input type not in the aforementioned page. While developers have stated that they'd like to implement and provide media library support for outside content, that has only been as part of similar conversations in the forums, and not part of any of the product materials.
In any case, you're welcome to request features you'd like to see implemented.
However, as to your statement:
That's not quite true. I could easily find a way to combine Channels as the backend to provide TVE and Locast sources to Tvheadend, which can also use your generated playlists and XMLTV guides for your 24/7 channels. Add in an SQL-backed shared library for Kodi to manage your provided media library, separate remote profiles for Tvheadend to selectively transcode high quality TV streams to lower bitrates (to mirror remote access), and you'll have it all in one program. (Not only that, but you can change the interface to your liking if purple isn't your thing; Tvheadend can selectively merge channels if you so choose, as well as rename or reorder them as desired.) and if what you want isn't available, you have the ability to add it yourself.
What you want is possible—it's just a lot of work to get a lot of different moving parts to work together. The question is how much effort of your own that you want to expend in achieving that goal.
