As I change lenses often I get a few specs of dust from time to time on my sensor and then it just struck me that if you just close shutter when camera is turned off then you could overcame this problem and this is exactly how film cameras do. Why not everyone does this in digital cameras?
Not sure about film cameras, but the shutter is an extremely fragile and sensitive piece of mechanics, and the consequences of damaging it are far worse than the consequences of getting dust on the protection plate on top of your sensor.
The shutter is closed by default on film cameras because if it was open it would have exposed the film while the camera is not in use - it's simply this way because there's no other choice.
In mirrorless cameras, the shutter must be open when the camera is on but not taking pictures because otherwise the camera can't show an image on the screen or digital viewfinder (if there is one).
Now, since the mirrorless camera shutter must be designed to be open most of time when the camera is on it makes engineering sense to keep it open also when the camera is off - this way you design the shutter so it's always open and only closes when it needs to - this is simpler (and so, cheaper) than it is to design a shutter that's open-by-default when the camera is on and closed-by-default when the camera is off.
And the shutter is not a good protector against sensor dust anyway, any dust of the closed shutter will be thrown off violently when the shutter opens (it opens really fast) and bounce around inside the camera until it sticks to something, no camera I know off has a mechanism to safely dispose of shutter-dust
On a modern SLR camera, it takes battery power to hold the shutter open. The power-free state is with the shutter closed.
However, on a mirrorless camera, the shutter is open out of necessity when the camera is on. It would not make sense to require battery power to keep the shutter open too - enough power is spent on everything else.
This means the shutter's power-free state is in the open position, and it takes power to close the shutter.
But atleast the shutter can be closed when you are changing the lens either by giving an option for that or by automatically detecting when the lens is removed.