If you have to leave an org for any reason, you lose access to the entire email history with that org. Some of which might still be important to you for a multitude of very legitimate reasons (such as contacts).
I try to forward important e-mails to myself if I think I'll need them outside of work (insurance details, etc).
I'm not usually concerned with what the employer does or doesn't want if they've decided they don't want me.
> I try to forward important e-mails to myself
They'll invariably be aware of this.
Your employer doesn't have to know everything about your business with them. They may think they deserve to, but that doesn't necessarily mean it needs to be true for you.
One might argue that this is a bit of deception, but it's also self-preservation of self-interest.