You could run trusted game server proxies. In FPS games this would help with the latency vs cheating trade-off.

1. An enemy is hiding behind a corner. The player takes a step and sees the enemy.

If the client knew the enemy was there, the player could cheat. If the client didn't know, the player would see the enemy with a delay. The proxy can share the hidden state at exactly the right moment.

2. When the player thinks that their shot hit the target, but the central server disagrees.

If the client is trusted to determine the answer, the player could cheat again. If the client isn't trusted, the player would sometimes see a hit that didn't harm the target. The proxy can make the decision and provide accurate feedback immediately.