How to use the WP REST API for new user registration (sign up form)?

Is it possible to create a sign up form that can work through WP REST API for visitors to be able to create accounts on my site?

I can create such a form and use it to create new users. This works with wp_rest nonce when I am logged in as administrator.

But if there is a visitor which is not logged in, the same form does not work of course. I think this is a question of authentication. Can you suggest a general idea how this can work? How can I allow visitors to be able to sign up with REST API?