As a drive expert, I can state that one reason for stall tension was to protect the expensive DC motor commutator when tension was required while the line was stopped. An example is on a paper winder. The number one priority for a winder operator was to assist in threading the Paper Machine after a web break. That left the winder untended with tension on. To prevent overheating a narrow portion of the motor commutator, tension was reduced.
It is profitable to establish tension as early as possible during the threading process. This allows the operators to concentrate on threading the remainder of the line. If the line is threaded using a reduced web width (tail, strap, etc.), it makes sense to begin with reduced or stall tension. Stall tension is very applicable for unwinds on a complicated coater or laminating line. When splicing, stall tension is often required to prevent tearing the splice apart.
If stall tension is used, there must be a ramped transition to run tension. This ramp should be initiated as soon as the web permits. The run tension may be initiated on going from thread to run mode, at a certain low speed, or when full width of web is on the roller.
Just because stall tension is available, does not mean it is should be used. An AC motor does not have commutator, so there is no need to protect it. Many lines are threaded without the drive and tension mode is not enabled until the full width of the web wraps the roller.
Furthermore, when winding on a core, the worst possible roll start is one with low tension for the first few wraps. This violates the Tension-Nip-Torque (TNT) principles for good winding.
The chart below shows an actual trend of the transition from stall to run tension for a paper winder/slitter that requires stall tension.