With local rendering, when you shoot a bullet you see the bullet shoot after local hardware latency (~50ms) and get a confirmed kill after local hardware latency + round-trip time (say ~50ms).
If the rendering is distant, the time until you will see that bullet shoot becomes 100ms instead of 50ms.
As long as the enemy player is remote, the enemy player position (and thus confirming a kill) will inevitably be delayed by the network latency (whether rendering is local or distant). That won't change.
The only thing that will change with remote rendering is that your own moves are also going to be delayed, which is certenly anoying I agree.
But, on the positive side, this ensures consistancy between the view and the model, that is: you won't try to shoot at a player that is not actually where you're seeing him. That happens a lot with local rendering.
If the rendering is distant, the time until you will see that bullet shoot becomes 100ms instead of 50ms.