I doubt it'd actually work. I'm sure a lot of the top-meta style decks in Casual aren't just folks trying to grind quests, but also folks who are trying decks new to them, but they're just top decks. Someone who's mostly an aggro player giving control priest a shot, but not wanting to risk ranks with an unfamiliar deck. So they'll queue casual, and removing gold/quest rewards will do *NOTHING* to stop them.
However, the major problem: it removes an avenue of play for folks who want rewards but who have ladder anxiety. There's a lot of folks who just don't like playing ranked modes. Don't **** them over.
If you really wanted a non-rewards mode, you'd need to split Casual in half, into Casual and Unranked, so that in Unranked folks could still get rewards, in order to not ruin things for folks who just don't like playing on ladders.
I'm aware I'm making a choice. I'd rather protect a player who hates playing in a ranked mode, over a player who just wants to play silly decks against silly decks. I don't feel at all bad about that, since none of us gets to pick our opponents, and if you don't want to play meta decks in casual while testing something silly? Bottom right, and requeue.
IMO it's correct as it is. If you play fun/strange decks, your mmr will be lower and you will fight against people like you. If you play casual with better decks, you will fight against powerful/meta decks.