The feds and other serious folks are pretty careful these days not to turn off anything until they've had forensics evaluate the situation. And not just because of FDE, memory analysis very frequently yields the best evidence due to it's timely and overlooked nature. Since most encryption systems retain their keys during lock and sleep, unless you usually leave your system powered off I wouldn't count on being afford…
If you're worried about a state-level adversary, then yes, you should always turn off your computer when not using it. They could still be spying on you and wait until you turn it on to kick down the door. There are people who have thought about these things, too. One suggestion is a dead man's trap, like a pad that you sit on, so if the door gets kicked down (or they snipe you from outside the window), as soon as you stand up (or fall off the stool) it scrambles RAM and shuts down the system. That's a super high level of paranoia, but still makes encryption useful.