Beeline is the most direct route and word is based on observation of how bees move back towards their dwellings after they’re done feeding on nectar of flowers. This nectar is converted into slimey goo which is enjoyed by us as honey.
As the crow flies is also a synonym based on how groups of crows flies back to their dwellings once they’re done with their business. I wonder if there are birds or insects who don’t follow direct routes–oh yes, bats certainly don’t as they use echolocation–finding path by using very high frequency waves which tell them about objects after getting reflected back from them–a very fine development indeed–because they can sense audio frequencies much higher than human audio range(20Hz to 20KHz). Echolalia is another related term–meaningless babbling of infants. Bats are only birds who are mammals too. Ostrich is a bird which can’t find the most direct route back to home as it can’t fly–though it can run super fast–can it beat Cheetah in agility? Cheetah is another word which is used in Hindi the same as in English. I think spots on its body (chitti–chitra) are behind the origin of its Sanskrit name.