Truth they could set it so the pilot would touch the paddle the K would start is work and synch it to the gear a bit later. You don't need the shift to happen as soon as possible, a delay of lets say 100ms is good enough. The important part is just to never lose drive so you can have that hypothetical 100ms delay is you have drive the whole time.
The problem is that you are limited with the rules i guess
The maximum permitted duration for down changes and up changes is 300ms and 200ms respectively. The maximum permitted delay for the latter is 80ms from the time of the driver request to the original gear being disengaged.
So I guess in this case you only have 80ms for the K to work is magic. But if that 40ms estimative is correct it could work, no?
I guess that is also the reason for that rule.