Maybe an app would replace those with notifications, which would be really nice. (I'm not good with coming up with features for an app, so try to suggest other features that you guys would like to have)
It looks to me that you're fishing for reasons to have a mobile app. Personally, I don't think that having a native app is worth the effort put in developing it.
To answer the example you mention, if you need help managing emails from lebgeeks, maybe all you need is proper filters and redirection rules in your mail reader? If you need help with this, don't hesitate to ask on the forum.