I've got the SCP-7050 and the LCDs stay on when I'm charging it. If I keep it flipped open, both LCDs and the button lights stay on. If I close it, the front LCD stays on.
Have any other 7050 owners experienced this? It seems like a counterintuitive thing to have the lights blazing while charging. I can't imagine it a good thing to have it like that while it's charging overnight.