That's what we do, using the Reply-to header, in case people hit reply. But the From header (which is what users see) still has to be one of ours. This is a requirement of SendGrid, AWS SES, etc., and it'd look pretty spammy otherwise.

Also, I just checked the latest notification I received from Facebook (someone posted on my wall) and its headers were

    From: "Facebook" <notifications+{code}@facebookmail.com>
    Reply-to: noreply <noreply@facebookmail.com>

This works great when the purpose of the site is to interact with other people that you know. It doesn't work for eCommerce or content/newsletters.