I'm a bit of a broken record regarding this but the key at the breakdown is making sure players stay on their feet. The Jackal doesn't necessarily have to be first to the tackle, he has to be the first to the tackle remaining on his feet. Far too often the team in possession send the first one or two players to secure the ball by flopping over the top of it then adopting a sort of "press-up" position to make it look they made an attempt to stay on their feet. I don't fall for it, these players are sealing off, preventing a contest for the ball so if an opposition player gets to the breakdown and stays on his feet he is entitled to go for the ball. If any of those players off their feet try to stop him they should be penalised.
Classic example was just before half time in the premiership final. Chiefs attacking, ball carrier tackled, Launch gets his hands on the ball, 2 or 3 Chiefs players try and drag him off but all of them were off their feet. Clear penalty for Wasps. Maxwell Keys of course, pings Joe.
Keep ALL arriving players on their feet and the whole situation is far, far easier to officiate. It would take a significant change in coaching but that's how the game evolves, they're already presumably adapting their tackle coaching to try and avoid red cards.