So, if their fuel gauge read empty halfway home, what were they going to do? Stop by the nearest "Shuttle Gas & Go" and fill up?
Explode. If those sensors indicate a full tank when it is actually empty during flight the turbopumps which supply fuel will super-rev and come apart like fragmentation bombs.
Of course if they "just" cut out when there is plenty of fuel they could just crash...
As I understand it the turbine pumps need to be shut down before they go dry, otherwise they will spin up so fast that they will fail spectacularly, with loose blades flying everywhere. The fuel sensors are there to gracefully shut the pumps down in the event of a leak.
This would cause an early main engine shutdown and an abort to low orbit, secondary landing strip, or a swim.
All of these are much easier on the crew than having the tail of the orbiter disintegrate at high Mach numbers and altitude...