> If it were really the case that there's an epidemic of invented reasons for warrants then parallel construction would improve the status quo by reducing the number of dubious warrants, leaving only those that "find something."

There must be an understanding here. A warrant executed for an invented and fictitious reason doesn't become "good" because it "finds something"; it's dubious precisely because of its provenance (a lie to cover an unconstitutional search). Whether there really is anything found doesn't impact the constitutionality of a search: that is the point of the "exclusionary rule" -- to exclude real, honest-to-goodness incriminating evidence of a defendant but which is found in violation of his/her constitutional rights. We cannot judge the rightness of a warrant based on whether it leads to useful evidence because then we would have no 4th amendment at all. Therefore, parallel construction doesn't improve anything; rather, it can only serve to increase the number of searches executed for fictitious reasons, and hence the number of dubious warrants.

nb: obviously, the above comment assumes/argues that Herring v United States was incorrectly decided. Also, I am not an appellate lawyer (or a lawyer at all).