Wow, that MC14500B (from 1977) is interesting. It really is a 1-bit microprocessor, with 1 input bit, one register bit, and 1 output bit. It's not a bit-slice processor, intended as a building block for a larger processor, but is designed for really simple industrial logic, such as "turn on pump if inputs A, B, and C are closed". It normally works with input and output latch chips, so you can use more that one input and output, and they get processed one bit at a time. Strangely, the program counter is on a separate chip (MC14516B), which is just a 4-bit binary counter. The application handbook explains how to do addition with the chip - by the time you deal with carries, single-bit addition takes 12 instructions! It's amazing that people actually could do useful things with a one-bit processor.

It is Turing complete. In principle it can do anything.

the program counter is on a separate chip so you can make it as big as your program demands.

The original Connection Machine was also composed of thousands of single-bit processors.