This is a concise and accurate summary, Joe--nice job. I agree on the prevalence of stat boosting, which irks me. It's a lot to track, and I have found myself too-often surprised that a small card shows up on the opponent's board with something like 15/20 stats. I think I don't get the right combos required to make this work yet. This aspect doesn't feel like strategy so much as memorizing combos and hoping for good draws.
Because of that, I don't like this "mode" of HS. I mean, HS itself is already struggling (for me) with allowing too much RNG, and Battlegrounds is full-on RNG, from the moment you're given two (often bad) choices about which hero you get to be.
It also doesn't feel like a "mode" to me because it's a completely different game. The pace, strategy, and manner of play are all totally different. If it's successful, I hope they simply spin it off as its own app, as I don't want to have to play it for challenges and rewards and the like.
Interesting new path for them to take, but it's not for me.