Cant you just revert back to using Gmail and not Google inbox? What you suggest is NOT trivial for the layman
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.
A few questions: Is Inbox actually less secure than the GMail app? Is there a reason why using Inbox (an official Google app) doesn't prevent these messages from being sent? And will these e-mails ever stop?
I don't recognize that exact notification text, but I suspect you're seeing the notification mentioned here (https://support.google.com/a/answer/6260879). As noted on that page, this is triggered by use of password-based auth (rather than OAuth). Is it possible you're signed into your account from Apple Mail using just a password?