I could come up with alternatives, as could anyone, but as you say they would all be imperfect so yes, you may as well stick with penalties to decide who goes through to the next round. (I think you dismiss awarding the result to the team committing fewest fouls too easily, but in a way that's a different discussion, about the role of referees. I like it because it rewards fair play and punishes cynical "professional" fouls, and the problem of diving and cheating already distorts results so it needs to be eliminated anyway. But I accept it's not going to happen because the authorities are too weak to deal with these problems effectively.) But my objection to penalties really concerns finals. I think that if two teams draw perhaps the most important match in their entire season, the result should stand. If commercial reasons prevent a replay, share the trophy. It's a game. No one will suffer. It will reflect what really happened, it would be the true result. I honestly believe the need for a victory when nobody actually won is a kind of infantilisation. It also relatively diminishes the achievement of teams who genuinely won the final outright, by beating their opponent in a proper football match rather than a subsidiary competition. I'm not as fanatical about it as all these posts make me sound, by the way! I don't spend long thinking about it. But I do think they are an unnecessary distortion of the game itself and I'd love to see them removed wherever possible.