On the full website, I click the title banner image all the time to hit the content display. It would be fantastic if the site name in the app's title bar was a link to the landing page. It's important to get there to search or browse site specific content. If I enter from a hot question or external link, it's not possible to use the back button to nav to it. If I've followed a few question links and the site isn't in my favorites, it's inconvenient to go search for it.
I'd suggest adding this link to places other than just questions, but I haven't found anywhere else I think it's called for. Search results use it as the dropdown to select search domain. Tag wikis and help pages don't appear to be implemented. The only thing left that merits an entire view is user profiles, and I'm not sure whether it's appropriate there. I wouldn't expect to be directed to the site's main page after clicking on a user's name.