How can chassis ground be used for voltage measurements in a device with components of differing voltages?
Things at different voltages often share the same ground.

When you say "If I wire the ground wire of a 30VDC LED and the ground wire from a 200VDC motor to a sheet of aluminum and turn it on, things are going to spark." you are making an assumption that is not necessarily true.  This is where you are getting off track: "Neither of these components can share a common ground because each is operating at a different voltage"

Ground can be the same for all kinds of voltages in the same system, the same way the ground itself can be used as a point of reference when measuring different peoples' heights.

Remember, ground isn't a voltage, it is simply a reference point against which other potentials are weighed.