This is a very important feature. For my other Company we sell Web Hosting services using WHMCS, and it has this feature we can see all the email communication which has been sent to the customer.
This feature would also help in case a customer says or claims something different from the email sent to him. I believe most billing/online software do have this feature.
I am also a developer and it should not be much work for Shopify team if they give the shop owners an option to add a BCC email ID w.r.t. any communication originating from the Shopify store.