is using the_posts_navigation() required?

The type of pagination you want to use is currently considered ‘plugin territory’. Users that download your approved theme must not be forced to use it. They may, for instance, have another system of pagination which they prefer. Therefore a theme must have the barebones pagination of the_posts_navigation() as a standard. It’s about ensuring flexibility to your theme’s users.

You may try to include your pagination as an option, as @majick suggests, but the formal approach would be to build your pagination into a plugin and recommend your users to install it with your theme.