I think that the waiting areas in Battlegrounds should have a temporary Armory Station you can use to swap your builds just before the match begins, and afterwards becoming inactive. When playing normally I use my overland/questing build, but that makes it annoying to participate in a random Battleground since I have to first get to an Armory Station to have a competent build.
I understand that ZOS probably doesn't want us switching builds mid-match, so that's why the Armory Station should be disabled once the match begins (or even disappear to prevent confusion). It just lets players easily swap into a PvP build in those seconds before the match starts.
Sure, they'll then have to deal with having a PvP build active once they get back to whatever they were doing before after the match, but (1) they knew what they were doing when they swapped into the PvP build to begin with, and (2) that only really affects the one player, whereas a random quester entering a Battleground with an incorrect build negatively affects their whole team.