I am aware, it is bad to run a water pump dry, the user manual usually says so.Sensing line cord current to restart, is fine if pump is wet, but could be damaging to motors running dry. It seems a brief couple second test every few hours should be well tolerated, but probably only of modest utility.
What is wrong actually ?
The only thing, I can see is cooling.
Water does cool the motor by the axle and housing. However, when running dry, the motor spins with little torque, hence draws little electric power.
These are two opposite effects about heating. The outcome is not clear to me.
No water has no effect on the motor bearings.
As far as I know, they run dry, whether the pump is pumping air or water.
May be water has an effect on the water seal at the shaft. May be this seal needs lubrication from a wanted tiny leak. I know there is an escape hole to make sure water doesn't go into the motor in case of a leak at the shaft seal.
So, running dry, may be is bad for the shaft seal. Recent pumps use ceramic seals.
Should we fear of the running dry syndrome ?