I have a backpack where the sleeve for the laptop pulls out completely from the backpack itself but stays attached with "rails" to prevent theft. I've never had an issue with this and never needed to place the laptop in a new tray. I fly once a month round trip in the US.
Not necessarily. My backpack, for example, has a laptop compartment that folds out flat. I don't have to remove my laptop, just send my backpack through.