I see on Commento.io it explicitly mentions being able to import from Disqus comments, but the "Import from a different service" is behind a signup wall.

Rather than signing up for a service that may or may not work for my site, I'm curious, does it allow importing from existing native Drupal and/or WordPress commenting systems?

That's my biggest pain point right now. Exposing public login to my CMS is a security risk (see: plugins/modules with permission escalation bugs) and frankly a pain I don't want to manage anymore. Migrating old comments to a new system is preferable to keeping the legacy comments system (and user accounts) in place while maintaining a second system on top of it for new comments.