It takes some getting used to but the operations by themselves are readable, it is just that what you do with them can be complex. It is like arithmetic. People usually don't have a problem with addition, subtraction, multiplication and division, but it doesn't mean they won't have a hard time dealing with complex equations.
Packing and unpacking are just some of the things you can do with bitwise operations. They are a common problem, and they are often tricky, so having an API for that makes a lot of sense. But if what you need to do is not packing and unpacking, I find it harder to understand the unpack -> string manipulation -> pack workflow than bitwise operations, it also tends to be more verbose and slower.
Packing and unpacking are just some of the things you can do with bitwise operations. They are a common problem, and they are often tricky, so having an API for that makes a lot of sense. But if what you need to do is not packing and unpacking, I find it harder to understand the unpack -> string manipulation -> pack workflow than bitwise operations, it also tends to be more verbose and slower.