I don't agree with the last point, the advanced metrics show Nurse is extremely high end at skating/carry the puck out of the defensive zone.
The NHL’s Top Puck Movers and Puck Transporters
While he may not have the greatest outlet pass, when he has the puck on his stick he is a horse skating it out, by far the best Oilers D-Man in those areas.
0.48 PPG the last two years for a d-man is not "flashes of an offensive game" ... that means if he got the top unit PP time and loaded up on McGravy points you're probably talking 45-50+ points.
How Klefbom only managed 0.5 ppg despite getting most of the top unit PP time and Nurse is only at 0.48 ppg (barely behind him) and even has more goals scored the two last years is hard to ignore.
Nurse's main issues are when play breaks down in the zone he can get himself out of position or in bad positions defensively at times and a lack of creativity offensively. When a situation is predictable and by the book he more or less knows what to do, but when multiple things break down quickly he can get himself into trouble. But you can the same for many d-men. He's not terrible but that's where his decision making sometimes suffers. When the puck is on his stick though that's not a problem. He has a good capability to carry the puck out.
He is a more old school type of d-man (90s/2000s era) with high end skating ability. That type of player can still play though.