Only partially. The much larger problem you are eliding is that there are multiple peaks of function and you are falsely assuming that there can be only a single one when you limit your observations to conservation. Catalytic antibodies are a fine example that refutes that assumption, as are regular antibodies.
Why don’t you try it with real-world, real-time data from catalytic antibodies?
Then it seems surprising to me that you would not have done so before going public.
I look forward to it. In the latter case, please don’t do as @Giltil just did and omit VDJ recombination and the fact that hundreds of B-cell clones react with a single antigen.