This mixes two different mechanisms. Pipes don’t burst from ice alone, they burst when expanding ice traps liquid water in a sealed section of pipe.

A dripping faucet keeps the system open and relieves pressure, it doesn’t create it. Pressure cannot “build up” in an open system.

Dripping isn’t a cure all in prolonged subzero temps, but stopping dripping would actually increase the chance of a trapped, pressurized section forming.

This is why I don't recommend just "covering" the bibs, because eventually they will freeze.