If they are so afraid of replays, maybe they should start slowly. Allow it only for offsides. Each team gets 2 challenges to either disprove a whistled offside, or ask for an offside that wasn't flagged.
If they are wrong, the opposing team gets a free kick from about 25m away.
Simple enough, try it out in Europa League or English Championship or 2. Bundesliga and see how it works...







