I think a more accurate statement is that the "San Francisco zoo....is phasing out." Period.
The small cat area was taken off of public view in part because the pathway leading to it did not meet current legal standards for accessibility (under the infamous ADA legislation), and the zoo was sued by "advocates for the disabled". It was cheaper to close than to fix, and most of the cats were sent elsewhere. But of course when the complex was originally conceived, it was to be an off-exhibit facility to allow development of new medium size cat exhibits, but that never happened and the zoo was pressured to open the utilitarian mesh cage complex instead.
There are still a few random animals in the chain link paddocks you mention, but they seem to be random relics that change regularly