Do you really think these emails are being intercepted by third parties? Surely the recipients are leaking them and no encryption scheme can prevent that.
I don't mean to say it's a bad idea, and it's standard practice in enterprise environments, but it's no silver bullet either.
Plus, to align with parent messages, it won't prevent leaking, it just helps to identify the person.
Or the senders, encryption being equally useless in that case, as well.