It appears that MSI has taken on a first with its 970A-G46 board and has added a VRM over-voltage throttling technique. The first point that made me aware of this was a reviewer on Newegg:
While it is not clear with this review whether it is really over-voltage throttling or another thing called Advanced Power Management (APM - I think it has to do with the chip temperature more than the VRMs and happens on all boards with FX processors), I took to the MSI 970A-G46 webpage and found that a BIOS update released in December added an "OVT protection function". The single VRM failure with the 8-core on the 970A-G46 was recorded in September, but there have been no failures since.
For the first time, I am marking down a low-end MSI AMD board as safe to use - however, I will also be marking its limited capacity with 8-core processors.