I think you got the order right in the alias and backwards in the reason.
Posted under General
If you look at the dictionary brooch has only one definition so of course it comes first in terms of use while broach has multiple definitions for which the synonymous definition to brooch comes last. Still when it comes to whether one uses brooch or broach at least in America broach is preferred. Brooch is never used in America unless perhaps it was in the distant past. I can only guess brooch was preferred on danbooru since a Brit was some how involved in the decision and I can only guess they may prefer brooch.