Assuming that the voting is fairly regular, removing the top and bottom scores and then averaging the rest would do nearly nothing, so there are no disadvantages. In this case where there are clear and unjustifiable outliers, this system would have helped remove stupid votes that were a result of some internal bias.
This is an interesting point, and it definitely would have been useful to use for BG4 and could potentially be useful for future judging. I still dislike the idea of using it with such a small amount of votes, despite their being no drawback to how results are generated. The only potential issue of this would be how this effects how judges determine their votes, but this is probably too inconsequential or even calculable to worry about.
Sere/chuck/nolem seem to be right to suggest this and overall I think that it would be a positive change, considering the overwhelming majority of sports judging have settled on this as a preferred method, it is probably good to follow this as well.
Also judges should be anonymous and if they leak anything they should be banned :-)