My guess is you never had to parachute into a project using operator overloading in strange, inconsistent, and undocumented ways with no original maintainers to show you the ropes

After all it's impossible to do this with regular code

I actually like operator overloading, but overloading the shift operators for I/O was still a mistake IMO. It's a mistake even if you ignore that it's a theoretical misuse (I/O and binary shifting have nothing to do with each other semantically). The operator precedence of the binary shift operators is just wrong for I/O.