I’m not questioning whether there is a market for this. I’m questioning the purpose and value to the user if it’s really nothing more than a snapshot of a dynamic site or just a site shortcut.
I agree on the 'auto update' aspect, but if you only update your CMS once every 2-4 months, it may not be that big a loss if there's no auto update right now.
I saw a demo of mulberry.toura.com and that was a question that came up - auto-updating. Apparently the iTunes store is a bit iffy about updating the apps if the functionality has changed too much, but if it's just content, it should be OK.
It works because you have to install a plugin in your WP blog, which presumably has WP publish/edit hooks etc which notifies an Appifier service, which then pushes to the apps, making sure all content is up to date and available offline. It's a pretty popular, if not the only, design for content surfacing apps.