I doubt that because it's probably illegal. Execs have to keep copies of things they write around.
EDIT: For those who are wondering, here is a quick summary [1].
Eric Schmidt's emails are definitely kept around a very long time, for very legal reasons, and whatever he happens to do with his own personal 'inbox' is not relevant to the subject at hand, and amounts to a kind of personal email/habit choice.
To suggest '72 hours' in response to a discussion about legal discovery etc. is basically misleading in that regard.
Execs themselves don’t, they just have to be kept around. The policies are most likely enforced through Gmail’s retention settings which are set by IT, who can view all of the mail (regardless of whether it was deleted from the user’s mailbox) in Vault.
Yes, of course, 'execs' don't manage anything on their own, but the OP is talking about 'email retention' in the context of litigation and discovery i.e. 'a copy' irrespective of label, which is a legal requirement.
Eric Schmidt is not deleting his emails after 72 hours for the reason you mentioned and certainly the company is not, which is the salient issue.
One could say 'oh that's just from his inbox' but that's pointless in the context of this conversation because we're talking about 'If the corporation has a copy or not' i.e. 'IT' etc..
Scmidt deleting maybe a local copy after 72 hours doesn't really have anything to do with anything other than his personal email habits.
EDIT: For those who are wondering, here is a quick summary [1].
Eric Schmidt's emails are definitely kept around a very long time, for very legal reasons, and whatever he happens to do with his own personal 'inbox' is not relevant to the subject at hand, and amounts to a kind of personal email/habit choice.
To suggest '72 hours' in response to a discussion about legal discovery etc. is basically misleading in that regard.
[1] https://www.spamtitan.com/web-filtering/email-retention-laws...