It's obvious that, even in this anthro version of the Fallout Universe, the Brotherhood just don't do 'subtle'... or 'strategy'... or anything really except 'blow shit up until we win or are all dead'. Without the Wanderer they and the Lyons, they were always more a joke than anything else. Let's face it, this is an organisation that thought a 20-year-old kid with a messiah complex was the obvious choice for next leader!
In any case, is there really any point risking their butts now? Let the Squealers and the Vaulties whittle each other down and, whilst the groaning winners are picking up the pieces, finish them off! Two for the price of one!
Yes, I know that's a Bad Karma strategy but I really don't care.