Birds do not come with exploding lithium batteries or large metal bodies like brushless outrunner engines do!
I do not think you understand how tight the tolerances are in a modern turbofan engine. Birds are relatively soft and get chopped up by the blades. Metal bits (like a drone will have) can break off or bend a blade. The imbalance of a broken blade will cause damage to the turbine instantly, which will cascade into further damage. (clearances are MILLIMETERS, if that, so any bending is a serious issue)