Is there a reason why kotlin doesn't have "regular looking" bitwise operators? (&, |, ~, >>, <<), I find it pretty annoying...

There is a reason — to prevent their abuse via operator overloading (think C++ and Scala). They might still be added at some moment in the future, though.

It's unconventional, but I prefer it because ^

Would be cool if those operators had warnings if overloaded, or if overloading was not allowed on them (which would kinda suck for BigNumber implementations, though)