I currently use Checker Plus for Gmail Chrome extension: https://chrome.google.com/webstore/detail/checker-plus-for-g.... Does the job very well.
Behind the scenes, it looks to me like Inbox is a new GUI on top of the same Gmail backend, so if the thread linking was fixed this certainly looks possible.
I don't know about assigned addresses, but for a long time Apple has used an imaginary John Appleseed.
As to why in-app purchase, I wanted people to be able to use it first without payment. In-app purchase has been growing in popularity on the App Stores lately and I think this is why. I also feel it's cleaner not to have two separate versions on the App Store.
But thanks for the feedback, I guess you're right. It's misleading to call it free. I will amend the landing page to make it clearer.
I know at some point they will switch to PubSubHubbub as the preferred way to get notifications.
