This seems like the ideal approach. The Segment theme component could be updated to add an option to include the provider_uid that is supplied by your Auth provider.
I’m glad you brought this up. The Segment tracking component currently has an option to add the user’s external_id for site’s that are using DiscourseConnect. Looking at it now, I see that it is using the old settings name for for DiscourseConnect - it is checking to see if the enable_sso setting is enabled. That needs to be changed to enable_discourse_connect. I’ll get that fixed tomorrow.