For teaching, paper and E6B are still very much a thing. But I suspect you’ll see it start to lean more and more toward use of EFBs, because let’s face it, they are becoming fairly ubiquitous and even those aren’t always used correctly or to their fullest potential. That some DPEs are likely limited in their understanding of the always-changing EFB environment contributes to this.
At this point, it’s still kind of a novelty like RNAV was in the early days, but it’s quickly becoming almost necessary to be able to properly use one - including mounting, charging, backups, etc. No different than the integration of the G1000 into everything in the cockpit - we have to know how to use these and all their manual reversion modes as well.
If nothing else, proper use of the old paper/E6B analog systems allow demonstration of a deeper level of understanding and proficiency about how to navigate an airplane. If you can use those correctly (while still flying), you’re doing really well and show that you will be able to apply those concepts to preflight planning and use of integrated NAV/FMS or EFBs. But they are quickly becoming utterly obsolete for practical use.
Personally, I’d like to see them used in conjunction during testing: show me both and use one to prove the other correct.