Part of SEO is, of course, to be reached. It’s one thing if people can find you on the web, but the second part is to let them reach you.
When I do SEO for clients, part of the process is to make sure they can be contacted on the web. Often, they have webpages or accounts in LinkedIn, Facebook, or Twitter, but many people check those pages only occasionally, if at all.
You should put your email address on all of your social media pages, incl. your website.
What about spammers? It used to be a problem 10-15 years ago that spammers scrapped webpages to get email addresses so they could spam people. But Google, Yahoo, Microsoft, etc. have pretty much put an end to that. There’s very little junk spam anymore.
My email email@example.com has been visible on the web since 1995. I get only two or three spam messages per day. But I also get emails from potential clients, invitations to speak at conferences, long-lost friends, students asking for information and help, and so on, which far outweighs the few spammers.
If you use LinkedIn, be sure to fill out your contact information. Add an email address that you check daily.