Re: The cynic in me says it's academic ...
"It's only in cases where the probity of the investigator is important that there's any risk - say, for example, a blood stained glove. And that's something that the judge can rule on and the jury make their minds up on. Which, by the way, is the current system in England and Wales. Evidence has to be acceptable to the judge to be admitted, courts don't just take everything the prosecution or defence brings."
Whenever the investigator is involved in gathering the evidence, his character is part of the validation of the evidence. Even in the case you stated, bank records, this could be called into question. Who is to say that he hasn't had an insider adjust the records? If he is willing to break one law to get the evidence he needs, everything he is involved with is suspect.
As for the judge and jury deciding on the matter, they can only do so if given the full facts. I'm not sure if it made it into the full IPA, but under a draft of it the cops were obliged to lie about the source of the evidence in some circumstances. Even the defendant was not allowed to reveal it, even having to perjure himself to keep it secret. That's not allowing the jury to make an informed decision.
Also, even without that, if a cop is willing to break the law to obtain the evidence, who's to say he won't lie about the source of the evidence?
The police should be held to a very high standard, because so much weight is put upon their word in court. As soon as they break the rules or law in the course of their job, everything they do is in question. If it's intentional, they could break other rules. If it's not, then have they been careless with other things?