Except if you add the MX records with a hostname of "www", they'll be used for emails to "your_name@www.example.org", which is generally not the desired behavio

Except if you add the MX records with a hostname of "www", they'll be used for emails to "your_name@www.example.org", which is generally not the desired behavior. And that still doesn't solve the issue with SOA/NS records, which need to exist at the root and thus will still conflict with the CNAME.