Minor White proposed the use of an incident reading technique in the Zone System Manual (Chapter 8: "Short Cut Exposure-Development Calculations") that is very similar to Phil Davis' technique. Minor White's method used the palm of your hand instead of a white dome, but it's all the same really.
Reflective metering, and spot metering in particular, is prone to error. Examples: Your meter may not have the same spectral sensitivity as your film, especially in the infrared. This can affect shadow readings dramatically (the meter picks up IR in the shadows that your film does not see). Spot meters are not flare-free, and measuring small areas of shadow surrounded by lighter areas may not be accurate or even precise.
Incident metering introduces consistency. Whether you meter from your hand or through a white dome or flat, any error caused by the difference between the spectral response of your film and the spectral response of the meter is systematically eliminated or at least dramatically reduced.
The leap of faith is in the way that the incident technique relies upon real objects having a limited range of reflectance. This assumption should be remembered when you are metering, and allowances made.
I guess that the required craft skill is in the optimum placement of the incident meter to take the highlight and shadow readings. I think that Phil Davis gives excellent examples of this in BTZS.
As Sandy says, I suspect that most of us use our judgement between the two methods. I work as a DoP/cinematographer, and it is normal for us to carry three meters - incident, spot and colour - and for all to be used.