You're right. The Roku app is mainly an alternate remote control. The only thing you can stream via the Roku app is non-premium content from The Roku Channel.
Many of your channels may have their own installable phone apps you can use directly.
Roku Community Streaming Expert
I am not a Roku employee, only a user like you. Please, no support questions via private message -- post them publicly to the Community where others may benefit as well.
If this post solves your problem please help others find this answer by clicking "Accept as Solution.".
Ultra 4800 | Streaming Stick 4K+ 3821 | TCL Roku TV 43S245/C107X