Salut Confit,
Regret I cannot remember exactly when the "white cross" (as I usually call it) disappeared after take-off. And I don't know if the logic ever changed. I don't remember ever watching the white cross after 100kts, even as PNF.
As you know, the only Airbus FBW I flew was the A320 family, but I'm very interested in woodja51's post. Until now, I have assumed that disappearance of the white cross may be part of the logic of the introduction of Roll Normal, and the gradual introduction of Pitch Normal. My old FCOM says these two processes start when the a/c becomes airborne, which implies the main L/G weight switches. But we know that the nose L/G also has weight switches, and woodja51 says the disappearance of the cross is now on that. I presume this may not apply to the A320 family?
So, woodja51, what about the control laws switching? Presumably, that still uses the main weight switches?
Returning to the original question, I think the white cross is useful for the PF at the very start of the take-off run (partly down, and not too much left or right). At 100 kts, when the PF has finished releasing the down-input, he/she may want to glance briefly to check that the desired aileron (if any) has been maintained. After that, forget it.