Competitive online games commonly predict the player's movement. Network latencies have improved and are now usually <16ms (useful milestone since at 60fps you render a frame every 16.6ms), but players expect to still be able to smoothly play when joining from the other side of the continent to play with their friends. You usually want every client to agree where everyone is, and predicting movement leads to less disagreement than what you would get from using "outdated" state because of speed-of-light delays.

If you want to predict not just position but also orientation in a shooter game, that's basically predicting the mouse movements.