Where you live online has become more important than your street address offline, unless you have packages delivered to you. Specifically, your e-mail address says more about you, and moves with you, than any other identity we can have. Because whether or not you have social media accounts, a website, a cell phone / text number, or the bills and banking for your home, you more often than not need an e-mail address to have them.
I also think it be important to have both a free mail address for your everyday lifestyle interactions, and a custom domain e-mail address for communicating with ‘live’ people in your life. With your own e-mail domain, unlike free-mail providers, you can easily move a domain to a different provider if need be. You can’t do this with your house or the address with which you live. And, in the United States, domain names count as intellectual property – they are legally protected. As with free-mail domains, you are forced to change your e-mail if the provider changes.
So, this is why I say that if your identity is important to you, and that people find you directly before using a search engine, that your e-mail address makes this easy to contact you straight away.