You said:
The typical system uses two rheostats in a Wheatstone bridge circuit to vary the current through the gauge's electromagnets.
Now, if the wire to the sender shorts to ground, the gauge reads full all the time.
If the wire to the sender breaks, the gauge reads empty all the time.
Either is possible, but the first is the deadlier, assuring the pilot that he has lots of fuel. The second creates complacency, since the pilot knows it's dead and ignores it and has no way of knowing if he has a leak or uneven tank flow. He might even believe that myth about it being legal because it reads empty when the tank is empty.
Suppose the gauges are good and they read a bit less than half. Are you going to make a habit of landing for fuel at half-tanks, thus shortening your range and carrying extra weight for no good reason?
Advice to accept defects in an airplane is never wise advice. This stuff is fixable.