You’ve skipped the actual first step. How did the B cell come to possess the receptor with a weak affinity for the antigen?
The function of antibodies is to protect the organism from invaders. If all you have is antibodies with weak affinity, you will die. The function is not present.
Fine. Accepting your calculation, that’s 12 bits for one antibody. And another 12 bits for an antibody protecting against the next pathogen. And another 12 for the pathogen after that. Or, if you happen to live in a malaria endemic region, 12 bits for the first var gene that a parasite strain expresses, 12 bits for the next, 12 bits for the one after that, until you cycle through a few dozen var genes possessed by that particular strain. And then start over when you get reinfected. As the process repeats, you very quickly exceed 500 bits of FI.