The fact that << and >> are big-endian is the "Benjamin Franklin mixing up the direction of current" of programming.
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Most binary processing is little-endian these days, because most processors are little-endian. Some network protocols use big, but I think that's shifting (Sia uses little-endian, as do protocol buffers, Cap'n Proto, etc.). I would prefer it to be displayed little-endian too.
Working with binary is sufficiently different from everyday base-10 math that I don't see familiarity as an advantage -- better to start from a clean slate.