Funnily enough, for my own toy CPU project I elected to make the program counter a GPR, both readable and writable - because it allowed me to eliminate jump and branch instructions.

Reads from the PC return the address of the next instruction to be executed, so a simple exchange between two registers performs the branch, and supplies the return address. (I did end up special-casing the add instruction so that when adding to the PC the return address ends up in the source register.)