When I use the P mode on my M10 Mark ii, the shutter speed seems to default to around 1/125 when using the mechanical shutter and to a much lower 1/30 when using the electronic shutter?
Might there be a reason for this, or is it something arbitrary?
It ends up as a quite handy way to switch between "P-mode for movement, P-mode for quietness "
Yes, there is a very valid reason.
Mirrorless cameras typically have an electronic first shutter curtain and a choice between electronic and mechanical shutter for the second curtain.
First, you should understand how a traditional mechanical shutter works. In the beginning, the sensor is covered by the first curtain. The first curtain starts to move down, exposing the sensor. Then the second shutter curtain starts to move, hiding the sensor. There is a maximum speed the shutter curtains can move. The flash sync speed of a camera is the fastest shutter speed where the first curtain is completely down yet the second curtain has not yet started to move. Faster speeds have a small moving slit moving down over the sensor.
Now, how could you make the shutter curtain electronic?
The first curtain is easy. The CMOS sensor pixels have a reset line. If the reset line of a particular sensor pixel is active, the pixel does not accumulate any charge from arriving photons. Release that reset line and the pixel starts accumulating charge. It is very easy to row-by-row deactivate the reset in a manner that you have a quickly moving electronic curtain through the sensor. The speed of the virtual electronic curtain has to match the speed of the second curtain.
However, doing the second curtain electronically is harder. There is no way to electronically make pixels not accumulate any more charge from arriving photons, apart from reactivating the reset line which destroys any accumulated charge. So, the only option is to just start reading the sensor pixels. Now, reading the sensor pixels is slow. If your camera is capable of high-resolution video capture at 30 Hz, the readout speed is probably around 1/30 seconds.
In contrast, a mechanical curtain can very quickly cover the entire sensor, allowing you to read it at whatever speed you're capable of in no hurry, without pixels accumulating any more charge.
So, the electronic second curtain is made by reading the sensor, which is slow. To match that, the first curtain has to be equally slow. You can have fast shutter speeds with slowly moving shutter curtains, but then you will have a rolling shutter effect.
My guess is that Olympus wanted to avoid the horrible rolling shutter with electronic second curtain shutter and replaced it instead with motion blur, directing the photographer to use instead the mechanical shutter when photographing fast action.
If you want to test the theory, try taking a photograph of something that is very quickly moving, such as a car. Do it first with mechanical second curtain shutter and then with electronic second curtain shutter. I'm sure if you use a fast shutter speed, you'll note the electronic second curtain shutter has a horrible rolling shutter effect.
Could you make a good fast electronic shutter curtain? Yes, you could. It requires changes to every single pixel of the sensor. By making the pixels more complex, you would:
One solution is a device where every second row has pixels sensitive to light, and every other row has pixels that are used merely for temporary charge storage. This approach loses half of the light collecting ability of the sensor, and half of the resolution of the sensor, while being more expensive at the same time.
It's hard to say what all is being set differently, and why, in P mode; sometimes the logic is kind of explained in the manual.
My best guess is that the camera is setting a lower SS in order to minimize/prevent banding with artificial lighting... 1/30 is 2x as long as the 60hz cycle of electric lighting (US).
