Your website is part of your branding. Your email is part of your branding. When people get in touch with you they need to understand that you're serious about your career. Anybody can be firstname.lastname@example.org, because that same person can be email@example.com and firstname.lastname@example.org. If people see email@example.com and go to johnsmith.com and see an actor's website. They know they're dealing with an actor... not an electrician.
When you get a website with your own domain name (i.e johnsmith.com), you absolutely should get a custom email matching that domain. If the company doesn't offer it, it means they're lazy as they have to manually go through the setup process. We know it! We do it. No excused.
You don't need to have a secondary inbox. You can forward all those emails straight to you gmail inbox, set up a label and deal with it that way, but it's absolutely more professional to have an email of firstname.lastname@example.org than email@example.com! Please don't email Princess Boom Boom and tell her that I used her email as an example.