We received a number of requests from (ex-)Clef users asking if we would perhaps build an authentication plug-in for WordPress, now that Clef is sunsetting.
This is our first version: We opted to use a proven extension as a base, and collect feedback. Then use that to develop a stand-alone plug-in in the future.
Yes! As a site admin in today's world, you should indeed not want to store passwords. Or even personal data for that matter.
I applaud this initiative since it lists exactly the reasons why we started Authentiq: Decentralization, usability, privacy, safety for end users (which is very different from merely offering security features that most people don't use).
Authentiq is similar in goals and architecture, yet with a more comprehensive feature set, since we aim to support existing standards (like OIDC) as the integration point for developers, and offer a more complete mobile identity to end users so that the site owner doesn't need to store those details either.
That said, I'm very keen to see if we can add support for the OP's authentication protocol soon. Check us out here if interested: https://www.authentiq.com/
There are probably several angles on this. One is to let our Authentiq ID mobile app support and sign in to SecureLogin sites. Another to let websites that use Authentiq automatically support sign-ins with SecureLogin. These look feasible at first sight.
A third, replacing our current auth flow with SecureLogin indeed isn't likely to work for reasons you mention.