I've read a number of stories on the topic - the basic technique is to identify the domain registrar or DNS provider and attempt to manually reset the password by spear-phishing with the customer service rep. Once you're in, MX can be redirected to a host of the attacker's choice, and then you can initiate password resets on any number of third-party services.
It's a vulnerability that simply doesn't exist with gmail/hotmail/outlook.com addresses. Do you know whether your domain registrar and DNS providers' CSRs mandate 2FA or allow multiple attempts at guessing security questions?
The reason I'd prefer my own domain is quite simply that I'd like to avoid being locked into a specific email company.