BE is not logical in any way, it is just a tradition, like the use of decimal numbers.

The use of automatic computers has forced a transition from the use of arbitrary conventions that did not have any logical motivation to the most efficient methods of data representation, like binary numbers in little-endian format.

Little-endian is more efficient even when you compute by pen on paper, if it feels awkward that is just because you were taught differently as a child.

There are special circumstances when a big-endian representation is the right choice, e.g. when you interpret a bit string as a binary polynomial, in order to implement an error-detection code with a CRC. However, for general-purpose numbers, little-endian is the optimum choice.