Hard to separate pending tasks from just conversations.
Hard to split conversations into separate threads when two topics diverge.
Leaving a conversation isn't just your decision: you have to both reply all and hope that no one else replies all using a previous email in the thread.
In a corporate email, inability to prevent mass emails from other employees. Hard to do for personal email too.
EDIT: I'm a huge fan, e.g., of the "travel bundles" Inbox creates. It's a giant win in usability for the use case of getting confirmation emails of booked trips. But you can see how it's a battle uphill that Inbox fights against the protocol, as the AI isn't always able to bundle all relevant information together, or extract key pieces of info from the email bodies.
