[gnode]

Bits are addressable, just not with a normal pointer. It would have been possible to have a special fat pointer for bits, similar to how C++ sometimes has fat pointers for member functions (depending on compiler implementation).

The restriction in C can only be explained as a limitation of the language itself -- although probably motivated by the implementation complexity it would require, for a niche use case.

[zabzonk]

I didn't mention pointers regarding bits, I mentioned addressability - a bit cannot have an address (in any language I'm aware of), though of course you can have any number of ways of accessing it.

[gnode]

Pointers, as a language concept, don't have to correspond to the addressing schemes of the hardware or ISA. On some architectures instructions may only be able to address aligned whole words. Some microcontrollers (e.g. Intel MCS-51) feature bit-addressable memory. Apparently, there's a special __bit type supported by the Small Device C Compiler for using bit addressable memory on such devices, although I don't know if it has support for taking pointers to these.