First of all - big thanks to developers for bringing battlegrounds to hearthstone and continuing its development. And since this game mode is still in “Beta”, I would like to allow myself some suggestions.
It could be possible to bring more freshness and entertainment in battlegrounds by doing events - (for example) once each month a weekend event (Saturday/Sunday) where all participants play a hero with same hero-power.
Common sense dictates that it is impossible to perfectly balance every hero, same goes for every other aspect of the game (“r” in “rng” is there for a reason). In such mini-event there will be possibility/opportunity for every player to be “more” equal and to “enjoy” Millhouse/Tirion/Brann or may be even Fungalmancer (one might go even further and make e.g. demon (replace with murlocs/dragons etc. if needed) invasion event with Jaraxxus hero powers for everyone and only demons in the minion pool - super balance is not needed - players might as well go “ham” during such event). During these mini-events regular ranking system would be on “hold” and may be even new 2-3 day rankings could replace that (or may be that could happen after monthly rating reset, since at the moment rating does not matter anyway). Players could earn rewards (e.g. car pack or two) by reaching some rating or by simply winning number of games. Regarding “hero portraits” that players could choose from - that might be simple aesthetic choice from 23 current WoW playable races (or may be thematic in every particular case - dragons/murlocks/pirates etc.). It could be a way to bring more WoW lore to hearthstone. If developers wish to bring in even more of this lore - these events might be even created as Darkmoon Faire.
In such case there are endless opportunities/possibilities to implement/introduce/start such events using carousel, fishing, death-match arena etc. And of course it would be subject to promote battlegrounds via mini-series in launcher and/or social media - anime or just using dressed up developers (asking for amazing once-a-month Jaina+Uther+Guldan style series that we had might be too pricey). Scenarios for those are easy enough to write, don’t know about creating costs though.
I am not sure how bringing of new(?) ideas works here, but probably many people have some to share and these were just few of mine (it is highly likely developers and/or other players have thought of these themselves anyway 
). Keep up the good work.