Roku Stream TV app should show same channels as the mobile app

We pay a lot of money for cable channels, including premium ones. First, Comcast won't let us use the Starz app, which means I cannot watch Starz/Encore programming on my Apple TV and Roku (and there are shows there that are not availble on OnDemand).

Second, there are several other HBO, Starz, Showtime, and Epix channels that are not availble in my TV listings, but are on the Stream website and mobile app. I do not like to watch TV on small screens though, which means I cannot simply turn on the TV and flip to what is on for all of the channels I pay for, plus you cannot airplay the app to the TV.

I thought using the Xfinity Stream app on my Roku would serve as a bandaid, but I do not get all of the premium channels I pay for on that app for some reason. How come the Roku app doesn't have the same channels as the mobile app and website? Why does Comcast make it so hard for me to watch the channels I pay for live on a TV?