If you obtain information that is not reliable, you can act on it (and convince judge to give you warrants) just probably not use it in real trial.

I also think it depends if you want more information for the current suspect or you are on a fishing expedition

Failing to propose a believable narrative for each increase in magnitude in the burden of proof may cause the entire case to fail in the US.

If you collect evidence on someone that would ordinarily require probable cause when that person should be enjoying the presumption of innocence, that evidence is inadmissible, as is all investigation that depends on it to proceed.

Parallel construction is taking theatrical steps ex post facto to defraud the courts into believing that evidence is not only admissible at trial, but also a reasonable basis for further investigation. If the FBI performs mass suspicionless surveillance on presumed innocent victims, finds evidence of a crime, then notifies another agency to contrive reasonable suspicion, then probable cause, to uncover the same evidence via a legally plausible narrative, that is kicking civil rights square in the teeth. Furthermore, it encourages otherwise innocent activities to be considered as reasonable suspicion, and promotes aggressive police tactics to manufacture probable cause out of reasonable suspicion, or bully people into providing consent or confessions. You get "judge dog" approving search warrants whenever the K-9 cop signals him to provide probable cause. And it combines with forfeiture to become even worse.

When "accidental discovery" evidence is admissible, that is a significant weakening of the public's protections against government, as it provides additional avenues for parallel construction, such as dropping a smoke bomb through a window and pulling a fire alarm, such that responding fire department personnel can notice "drug paraphernalia" and tip the police, who get a warrant based on the tip and conduct a search for drugs. This encourages obstruction of services to promote public safety, such as disabling alarms or blocking emergency calls. When "clean hands" evidence is admissible, one "dirty hands" cop--or a paid informant--just needs to pretend to be an anonymous member of the public to tip off the "clean hands" cop. My own non-judge opinion is that poisonous fruit is when one law is broken in pursuit of enforcing another, not just when someone's rights are infringed.

Presumption of innocence isn't directly enshrined in the US constitution. Local prosecutors and governments can and do abrogate it.

The SCotUS opinion in Coffin v US stated the following:

  "The principle that there is a presumption of innocence in favor of the
  accused is the undoubted law, axiomatic and elementary, and its enforcement
  lies at the foundation of the administration of our criminal law.
  ...the exclusion of an important element of proof can be justified by
  correctly instructing as to the proof admitted. The evolution of the
  principle of the presumption of innocence, and its resultant, the doctrine
  of reasonable doubt, make more apparent the correctness of these views, and
  indicate the necessity of enforcing the one in order that the other may
  continue to exist."

They can also get away with doing the exact opposite in their practice, only to be overturned at great personal expense to individuals with few resources.