...a few Mylar balloons would do the trick and would definitely cause a major BES line to relay.

or a stick. but you have to be pretty brave: https://www.youtube.com/watch?v=6fGdZ-nu7zo

Protection systems (breakers and the like) trip via heat. The point is not to let so much current flow through your hardware that your hardware melts. Tree branches have high resistance. A short caused by a tree branch will not pass enough current to be a problem, just set the branch on fire.

SOP for fire departments responding to branches on lines that haven't brought the lines down is to call the utility then babysit the tree branch until it finishes burning.

modern protection on power lines do not use thermal Magnetic circuit breakers like the panel in your house.

The current passed by a tree branch depends both on the resistance of the branch and the voltage of the line. In the video I linked it was clearly enough of a short to ionize the air and cause an arc that would damage equipment quickly.