I see. In that case, yes it'd make sense to have such a feature, probably implemented as an archive button in the incognito window (with a warning that archiving such a chat makes it non-private).
For Google privacy is a problem, since they want as much data they can get. So they've put in "incognito" so it sounds modern enough what competitors have with E2E, but they'll try and make it inconvenient and not default as much as they can.
Of course they won't be open about this, because they're making the world a better place <insertcuteemojihere>
Why can't it store E2E chats locally and never upload to google, or even encrypt with a passphrase like Chrome sync does?