How about simplifying it even further? There must be a few cards that are widely disliked. Donald is probably in the best position to determine which ones - have him pick 3 of them. Then in the matching screen add a criteria of "play with banned cards" so that people who really want to play with them will get matched with others that want them also, and no one else will have to see them again.
I doubt this would affect ratings because we would all have the same choice to make: a simple yes or no to a fixed set of cards.
I suggest banning Possession and Rebuild. Those are the only two I really dislike, but I'd be happy with the above proposal whether it banned those cards or not.
Why do this when people could just select the ones they don't like? The mechanism is already partway there with Familiar Cards. It seems simpler and more player-friendly. I don't think anyone could "game" this feature in any meaningful way.
I thought the primary argument against allowing people to ban cards was that the rankings would lose some of their accuracy. By only allowing a single, common set of cards to be banned you greatly reduce that possibility. If it turns out that there is a significant advantage to playing with the banned cards, or without them, then we'll all know it and those that care can play with the better option.
On the other hand, maybe choosing which cards to ban will become a meta-strategy that deserves to be part of the ranking system.
If it's only 4 or 5 cards (as has been suggested) they can block, any inaccuracy is likely negligible, as the game has hundreds of cards. Like, what advantage are they gaining? Making it hard for a certain strategy to come up? There are just so few cards that have no analogues, and even if something unique is getting the shaft, is there really any harm? After all, Possession is the most hated card. At worst, someone could block, for instance, all coin token cards and remove that element from their games, but I doubt every single person would ban all of those cards.
I can see the argument "everyone should be playing by the same rules down to the letter" if the competition is super serious, but I feel like we are here strictly to have fun at the moment, and this feature would make the game more fun for people. Even if that becomes an issue, serious tournaments could always be run without the banlist. At any rate, I feel like I'm basically just repeating Donald's posts, and I generally trust him, so if it's good enough for him it's good enough for me. (that's just my 2 cents)