As of WordPress 4.9, the administrator cannot change the site admin email without outgoing email setup on the server, and recipient email credentials. This plugin restores the admin’s ability to change this setting without sending a confirmation email.
Plugin in the wordpress.org repo:
As a bonus, for developers I’m distributing some BDD Codeception tests with this plugin. The tests are designed to run via the WordPress module from Codeception. To run them, you’ll need composer, selenium, and chrome. To pull the framework, use the instructions here.
When building this, I used TDD / BDD by creating an acceptance test that worked on v3.9 so that I could run the same test against v4.9. This is overkill, but I wanted to show how to run tests against different environments.