With the annulus closed, produced fluid stays in the tubing, and the annulus can be used for lift gas, for a fluid cushion, or for monitoring. Packers are set by mechanical manipulation of the string, by hydraulic pressure, or on wireline.
A packer that does not hold turns a single completion into a leaking annulus. In a gas-lift well the packer is what keeps the injected gas going through the valves into the tubing instead of escaping up an open annulus. It is a completion item, not a piece of the drill string.