It should be unstable because in a polytrauma patient who is unstable, you have no idea where they are bleeding. Taking them to the OR for a laparotomy when they could be bleeding to death from a pelvic fracture or femur fracture, or have spinal shock, makes little sense. So you FAST them to see if their cause of hypotension is from an abdominal bleed, and if so, take them to the OR. That was the intent of the FAST. FAST essentially replaced the DPL as a means of determining if the abd was the site of bleeding in a patient unstable for CT.
However, since its inception, it has become pretty standard to do a FAST on all trauma activations.
Here is a blurb from ATLS on FAST:
FAST, eFAST, and DPL are useful tools for quick
detection of intraabdominal blood, pneumothorax,
and hemothorax....The finding of intraabdominal blood indicates
the need for surgical intervention in hemodynamically
abnormal patients. The presence of blood on FAST or
DPL in the hemodynamically stable patient requires
the involvement of a surgeon as a change inpatient
stability may indicate the need for intervention.