Nice to see the COSMAC 1802 mentioned somewhere. If you look at my article "Calculator Memories from Argentina" in the Memories Forum here at the MoHPC, you can see a photo of my COSMAC homebuilt development kit interfaced to my HP41C by counting the pulses generated by TONE instructions.
While the COSMAC was truly static and low power (and had those FLAG pins with their own instructions to test them), I would like it to have a second accumulator. At the time, most of my collegemates were favoring the 6800 - 6802, but my COSMAC would run on batteries, could be stopped and did not requiered a monitor in ROM to work (because of the LOAD mode). Nice memories, nostalgia again...
My COSMAC used two 5101 CMOS RAM chips, which gave it 256 BYTES of non-volatile RAM. A mercury button battery (not environment-friendly, but nobody was aware of this in 1980) sustained the RAM contents for many years in standby mode.
I think most of the initial microprocessors, apart from the COSMAC and the Motorola "1-bit" (!) CMOS CPU (was it the 14501?...not sure) have at least some dynamic circuitry inside, which prevents their clock to be fully stopped. I may be wrong, but I think that was the case with the 8-bit designs from Intel and Motorola around 1975-1980, which were not CMOS either.
I am still in debt with Dave Hicks and the MoHPC, because I have had not time yet to try to find and post here my (very primitive) cross assembler for the COSMAC, which ran on the HP41.