It’s Amazon’s internal network, and Amazon’s email system, so they have the full right to control what happens on their resources.
At the same time, I find that deleting the an email after it has been sent by the sender unknown to the sender to be a kind of gaslighting, and dystopian. Having a policy to not organize using work resources might be harsh, but at least it is more transparent as in the proverbial line is drawn in the proverbial sand.
It's against Amazon's interests to have this organization happen in a parallel, side channel instead. But they seem to be pushing this action in that direction.