I am not sure. We may be more sensitive to smaller misalignment looking down at a spinning triangle than out at the world. If I get a "go!" and it is 10 degrees off, I will still be following the correct street in the correct direction.
The problem is that the compass won't be off by just 10 degrees -- it could be off by 90 or more degrees because of overhead wires or the magnet in your wallet or anything else nearby that happens to have electricity flowing through it.
Oh, for sure there are degrees of wrong that would break any reliance on the compass - no question. My point was simply that this approach may have better results sooner.