It is a capital mistake to theorise before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts. (Sherlock Holmes - A Scandal in Bohemia.)  I agree with Artisi.  Sounds like the suction line is blocked giving lack of NPSHa.  On the cooling tower duty I presume you have a flooded suction?? Try fitting a combined pressure / vac gauge to the pump inlet nozzle or as close as possible. Close down the pump and take a pressure reading and record it.  Start up the pump, let it settle and then take a further reading. If you see a negative or reduced pressure and the suction line is fairly straight with no close elbows or valves you will probably have a line or inlet restriction.

The reason why air dampens the cavitation is that air in a liquid is a poor transmitter of sound.  The cavititation is still occurring I'm afraid. The damage varies with power. As a rule of thumb, double the power; cube the cavitation damage.

Most pump problems can be resolved by fitting calibrated suction and dely  gauges plus a strap on ultrasonic flow meter (if appropriate) and an understanding of pump curves.Multi-stage pumps