Rockets can easily accelerate with enough force to kill a human (cargo flights and unmanned flights use different launch profiles for this reason).

The less Gs you need to design a component for, the lighter/simpler it can be, so why unfurl early and add that extra mass and complexity to the design?

When rockets are firing lots of acceleration is applied that the delicate structures are only designed to handle when stowed. Think long arms on hinges. They can take acceleration in one axis, but not at 90 degrees to it.

The parts of a ship that thrusters are directly attached to experience acceleration first, the other parts that are further out from the thrusters won't accelerate immediately and if the acceleration is too sudden or extreme could be damaged or break off entirely.

And to answer your question in the other response, many thrusters have a minimum thrust, and even that minimum may be too much for the parts when deployed.