It's not uncommon usage of the tab bar. For example on iOS, the tabs are solely used on the main page.
Pulley menu is not very handy for navigation between many pages. Pulling the menu to keep switching between views just doesn't work. There are several drawbacks for having the navigation list on another page: (1) you need to swipe to the list and then tap to choose as opposed to just one tap on the tab bar or swipe to change tab. (2) it hides the state of the app (3) it hides the possible pages from the user (4) it is not possible to conveniently inform the user about new updates on each page.
I listed these already in pros in the original post.
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