I have been a big fan of what I like to call the "Shake the $*!T out of it" method of degassing. My thought on this would be that it really is more pure degassing, as there should be little to no oxygen in the headspace after fermentation becomes active. I would say as well, this certainly rouses the yeast.
I oxygenate at the start of fermentation using pure oxygen and a diffusing stone, and I do believe this is an extremely important part of fermentation management. My understanding has been, however, that oxygen after the initial aerobic yeast metabolism and cell division, oxygen is not necessary, and may even be detrimental.
Here's my question though, and it comes from your statement regarding "adds some oxygen to encourage yeast health:" Is there some actual *need* for the yeast to have access to oxygen after the initial stages of fermentation?