This thread is such a classic read. It really hits on that tension between traditional ‘local knowledge’ and the tech we rely on now. Even with all the triple redundancy and Kalman filtering in modern DP systems, there’s still something to be said for just looking out the window or having a simple analog reference. I actually keep 123compass.org bookmarked on my phone for those moments when the gyro starts acting up and I just want a quick, independent ‘sanity check’ on our heading without overcomplicating things. Sometimes the simplest tool is the one that keeps you from heading up the wrong fjord!
The writer James C. Scott in Seeing like a State used that same analogy, the way a pilot navigates with local knowledge directly using the senses vs using a representation such as a paper chart or ECDIS.
On a steel vessel, I don’t think I would rely on an uncorrected, handheld magnetic compass app like this. 
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Why is that better than the compass app that any iPhone has anyway? As mentioned, it could provide interesting results on a steel boat.
A tension can arise depending upon differing levels of expertise of the watch officer and the nature of the tools and instruments.
For a watch officer that is competent with tools such as the compass, the radar and the anemometer, using those tools become an extension of one’s senses.
On the other hand becoming competent with tools like ARPA and ECIDS, tools that create a representation of the real world, can limit the acquisition of other, "seaman’s eye-type skills. Tools like ARPA and ECDIS, should be used to develop and refine the “seaman’s eye” rather than replace it.
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The question is which navigation-related tools are appropriate, at the margin, in any particular context.
It all started with the anemometer, a good example might be the capsize of the yacht Bayesian with the tragic loss of 7 lives.
The yacht was anchored at night, with a deck hand on watch. The captain wanted a call when the wind speed exceeded 20 kts.
Of course a deck hand might be able to judge the wind speed at night from various observations (feel, vessel motion, sound, wave height etc) but observations combined with a anemometer is going to be more reliable and precise than observations alone.
Reliability is important given the vulnerabilities of the Bayesian, taking prompt action in the event of high winds was critical. Precision is important because the captain doesn’t want to be awaken for 15 kt wind and from 20 kts to 28 kts wind force is doubled.
The same general point holds wrt the ECDIS and ARPAs, the compass and so forth. Competent use of Instruments combined with skilled observations is better than either one separately