> Calipers need to hold memory specifically.

You don’t need power to retain a tiny bit of settings data.

I believe the real reason is because most of them have the “helpful feature” of turning on when you move it. Without something monitoring the sensor, no way to know to turn on automatically.

No, most calipers can only do relative measurements. It’s constantly counting how many 0.01mm the head has moved so it doesn’t lose track of where 0mm is located. Turning on the LCD when the volatile counter changes value is a free feature since the mcu is always on.

Of course better calipers do absolute measurements, but they’re too expensive to scribe lines with and therefore useless for hobbyists.

It is not just hobby people scribing lines. Just saying.

Memory of what?

Probably which position the zero is at, and maybe which measurement system you're using.

The zero set-point, usually.