Comment by ttimebomb

Some do, but its much more expensive for game companies and adds latency to some elements. Its generally a much harder problem for first-person shooter games - an enemy might be hiding behind a wall but the game needs to know the position of that enemy anyway because the player might move around the corner and see that enemy before the server updates or their game client might need to play noise that enemy is making faintly even if they are far away.

Players of these games are sometimes running their games at high framerates like 240fps which is much higher than the tick rates of these games too.

Plus it doesn't solve all the possible cheats that are out there, as there are some like aim-hacks that don't need any server information to work.