My previous employer did this, and no one seemed to miss it. If you had a use case to add an exception (the most common was to send yourself a mail from your personal Gmail, to print something on the corporate printers) that was supported and straightforward too.
One solution would be whitelist only. You must specifically whitelist a domain or email address, and everything else is blocked. If someone wants to send you an email, you must get their email address.
However, if you are using it to sign up for a service online, the domain often does not match the sender. You might sign up at the example.com website, but you get an email from [email protected] as the email address.
