While I did lose access to a hosted email and other services, and only permanently lost access to a free domain name so far, also was close to losing access to regular paid domains on multiple occasions (once because of the used registrar, twice because of the place I live in and international politics, being disconnected from payment systems, though with registrars also contributing a little).

Mandatory reliance of services on other services (whether it is email, phone, or a more explicit identity provider) is generally unfortunate. I think it is best to not look for a perfectly reliable setup, as it is unachievable, but to keep in mind that they are not reliable, to have recovery plans and fallback options if possible, reduce dependence on online services, especially those depending on others. Though a personal domain name still seems more reliable to me than that of an email provider.