Each context will have a mobile-first or desktop preference. In my context, yes. Most of the students are more comfortable accessing web data on a mobile device. A majority of the first-year students do not have their own laptop or desktops. It is more common for a student to have a desktop at home and then use their mobile device everywhere else.
I really wanted the mobile app to work. In truth, the mobile app does not work well. It crashes frequently, and I see a page with the error to check my internet connection with the AJAX spinner. Additionally, the mobile app does not support some content types. Furthermore, the app does not play youtube videos natively. Instead, it redirects the user to view it on youtube.
From my limited testing, using Chrome or another mobile browser provides a better experience than the mobile app in the current state.
My opinion is for you to focus on the main features of Tutor and add improvements to edX, such as additional plugins. The web-view using a mobile browser is good enough.
If the Android app functions better than the mobile browser, then having a single Tutor-branded app in Google Play is my preference. Branding is not a problem. Honestly, I don’t want to go through the hassle of releasing a custom version. A generic Open edX or Tutor logo will suffice. Perhaps upon opening the app, the user could type in the URL the instance and then login.