The problem I have with parallel construction is that it rewards potentially illegal behavior on the part of law enforcement and prosecuting attorneys in a manner that's difficult to police.
"Parallel construction" doesn't just mean "look for other evidence of the same crime", it involves keeping the existence of the original, inadmissible evidence secret from the defense and the court, then constructing a chain of events that plausibly would have lead to incriminating evidence without knowledge gained from the illegal search.
Among other things, this secrecy deprives the defense a reasonable opportunity to argue the inadmissibility of the new evidence on the grounds of it being the fruit of the original, illegal search.
Note that I say "argue" — there are right ways and wrong ways for law enforcement and prosecutors to "work around" tainted evidence, but if the existence of tainted evidence gathered in secret is routinely hidden from defendants and courts, it becomes very hard to hold anyone accountable for going about things the wrong way.
"Parallel construction" doesn't just mean "look for other evidence of the same crime", it involves keeping the existence of the original, inadmissible evidence secret from the defense and the court, then constructing a chain of events that plausibly would have lead to incriminating evidence without knowledge gained from the illegal search.
Among other things, this secrecy deprives the defense a reasonable opportunity to argue the inadmissibility of the new evidence on the grounds of it being the fruit of the original, illegal search.
Note that I say "argue" — there are right ways and wrong ways for law enforcement and prosecutors to "work around" tainted evidence, but if the existence of tainted evidence gathered in secret is routinely hidden from defendants and courts, it becomes very hard to hold anyone accountable for going about things the wrong way.