WP core uses an older version of jQuery for the purposes of browser compatibility, since it is part of its mandate to support older browsers.
There are many ways you could include jQuery in your WP project and manage its version. The most straightforward would be to enqueue the script as you have suggested and update the script manually as needed, but you could without much difficulty set up a package manager like Bower or npm Browserify to automate the versioning process. See for example https://generatewp.com/automation-wordpress-practical-guide/