If you draw a free body diagram, weight is down and thrust is forward. Both force pass through the center of mass so they don't impart any moment to the rocket.

If you draw a free body diagram, weight is down and thrust is forward. Both force pass through the center of mass so they don't impart any moment to the rocket. So it has no tendency to fall over. They do impart a net horizontal force so it has a tendency to run away sideways. For the broomstick, weight is down but "thrust" is both up and forward. So there is a moment caused by weight at the CoM and up-force at the base.