Have you ever given someone climbing hard climbs?
At 5.6, a climber can take minutes to place a gear, few more minutes to test and final clip.
At 5.12, a climber might be on overhang and place a gear and clip in less a minute sometime.
Belaying someone at different grade is entirely different and a belayer should be trained for safety. You might as well be certified for each grade instead of one certification thinking you are done with belaying.
I have improved my belaying but still need to be even more amazing at belaying.
Why? It is because you can save your friend from injuries and unnecessary long falls.