Hi, Gmail engineer here.

This isn't specific to Inbox; we have limits in place for all accounts (documented here: https://support.google.com/a/answer/1366776).

You can probably understand why this is necessary to keep our systems healthy--while the vast majority of users never encounter the limits, if they didn't exist, there's a risk that abnormal usage could limit our availability for every other user.

That said, I think the request to make this more obvious to the user is a really good point and something I'll look into.