Left to my own devices, and not constrained by school standardisation and the test syllabus, I'd teach integrated PLOG and GPS, then do diversions "no screen". In practice I have to do it the other way around somewhat - screen only for traffic and airspace, not navigation most of the time, and bizarely students CAN use VOR on a diversion but not normal nav. Standards are slipping, very badly, and I suspect were poor in the first place - the present odd approaches to teaching aren't helping at-all.
In the last few months I've had a 45hr student move from another school, who had no personal culture of keeping data on a kneeboard. I've had another who passed his PPL within the last 3 years, doing his NQ with me, unable to find his way to our base airfield at night when I went "no screen" (I set up that situation with a very visible motorway going all the way from A to B, and he still couldn't handle it). At the same time whether it's SD, a GNS, or some other tool, far too many pilots - student or already qualified, just won't actually put the effort into learning the device they're flying with. That's no better or worse than using DR nav and not learning the tools of that properly.
I have become a big fan of SkyDemon (and yes, you can check the database is up to date), I just don't rely on it absolutely, nor will I let my students. Very happy to see a route on SD, I just want to see it on a chart and PLOG too, and if the device fails, I expect my students to be able to complete the trip, or make a safe diversion. Maybe a bit less elegantly, but still complete it.
G