Kind of, it's different to trust a big company instead of a particular person. I have had the same email since the creation of Gmail, free, and I can create another with a custom domain and configure it to forward all messages to the custom one or backward. Could be the same here.
You don't own either a domain, is just a rental really. If you can't pay for it for some reason one year, it will be released, probably at a much higher price. I rather have a free email as a base, even if I use the one that I have a custom domain for.
Absolutely agree but it's the lowest level of the technical solution we use for smtp mail control available to the public. Whoever owns the MX record control owns where mail is delivered. Your mail is likely the common key to most of your identity since it's used for recovery.
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The same should be true for social media services. Maybe not your domain, not your identity applies....since you don't control it.