Storage space is so cheap and free now. And none of you have more emails than could fit on a $4 jumpdrive.
You can even just go to Google Takeout[1], and have it export all of your emails to your associated Google Drive account. You can store up to 15G. You don't even have to worry about finding a place to store it. Takes only a few minutes. And no time limit to download the archive from your Google Drive.
Why is this painful for any of you?? You can easily make a backup, AND also declutter your account.
I almost feel like some people are so committed to minimalism that they are forcing themselves to needlessly purge precious memories just to prove a point about how hardcore they are about throwing things out. So I feel bad bursting their bubble that this sacrifice is pointless.
[1]: https://support.google.com/accounts/answer/3024190?hl=en