[Raphaellll]

Another problem of predicting the movement of other players is that if they stop before you can see them, the trajectory would be interpolated further such that you can see them around the corner for a split second, knowing they are waiting there.

[ggambetta]

The technique I describe in the article strictly interpolates between known positions; it never extrapolates further, so other players would never be seen or rendered beyond the point where they actually stopped.

[Raphaellll]

Yes, I got this. Just wanted to point out that a particular consequence of extrapolating would be that players can see enemys around corners. You already mention that the game would be unplayable if players get teleported every few ms, and above just describes why, aside from aesthetics, makes it unplayable.