To me this smells 100% like a transient issue, Gigabyte probably assumed that more phases would wipe the transient response time out. The issue is that if you're shutting down phases as Buildzoid mentions you'd have to do to get efficiency; you then lose that response time advantage until the phase is spun back up which is the longest part of the power system cycle. Normally output filtering is designed to make up that gap, but I think in the case of these chips that's not happening. I suspect it's a lot more complicated because I have a sneaky suspicion that adding more caps wouldn't solve the problem (completely).

This mobo has 16 real phases, according to BuildZoid's analysis.

I imagine it is. I meant they had such issues in the past (hence the "this time for real" approach) so it may be that they cut different corners in order to meet some other targets that are marketable.