In: Biology
1.if you like to have an assay, which also gives a signal from the weakest immune response, that would mean, that your assay will have to show also low affinity binding effects. In that case you will not get rid of cross-reactivities and other potential interference effects, but you will have positive results even in earlier stages and with weaker immune responses (maybe false-positives due to cross-reactitivies of unknown molecular reasons).
2.For many diseases and situations the weak immune response is not relevant. Unfortunately most kit manufacturers and also scientist do not realize and mention this difference in the intended use and the answer of an assay.
Again: It is a question of your research task, whether you should avoid potential interference due to cross-reactivity and similar effects or not. You can avoid it by using interference-reducing assay diluents or antibody diluents. But this is not always good to do so.