I think you just made that up without doing any math. Far more likely is that the ruggedness of fitness landscapes differ by orders of magnitude for different antigens. Yet mutation+selection finds a way.
So on a similar subject, why did you write,
Keefe and Szostak did just that. They created a library of 6 x 1012 proteins each containing 80 contiguous random amino acids and then estimated that approximately 1 in 10^11 random proteins bound to ATP.
Why did you omit their very explicit, quantitative qualification of that, Gil?