Hearthstone is a fairly simple example of the TCG genre. I consider that mostly a good thing, but it does mean that the game can feel repetitive and stale once you've seen most of what it has to offer. The weekly Tavern Brawl format helps to keep things fresh, even though it's not something you'd want to play all the time.
Learning what the new rules mean is part of the fun of playing in the Tavern Brawl. You know what the rule changes are going in, but I find that I almost always see something unexpected in the first few games that I play under a new format. The implications of the rules modifications usually go deeper than my first reaction to the obvious differences.
Just about every one of the Brawl formats I've seen fall into one of two categories: horribly unbalanced, or massively random. After a few games, it's usually pretty clear why these aren't the standard rules! Some formats heavily favor one class or deck type or players who have lots of high-end cards, while others add so much random activity that the player's choices feel unimportant. These are fun to play a few times, but you wouldn't want to do it long-term. So it's good that the Brawl only comes around once a week, and don't repeat very often.
The rewards for playing in the Brawl are simple: one pack after winning one game each week. You can also progress your quests and 1-gold-for-3-wins objectives. This is a nice balance, because it encourages folks to play a few games, but doesn't provide incentive to keep going past the point where the fun of discovering the new format wears off. If you get tired of the Brawl after winning your one game, you can simply return to Arena or constructed play, without missing out on any rewards.
I can't recall seeing anything similar to the Tavern Brawl in any other TCG that I've played. Modifying rules occasionally does happen, but not in the structured and recurring way that Hearthstone does it. I really like the way it works, and I hope the developers keep coming up with new and interesting ideas for the Brawl.