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"Police officers are not trained lawyers and may not appreciate the nuances of what would or would not be admissible or relevant evidence."

That is not my experience. Senior police officers are more than capable of distinguishing these nuances and junior police officers are rarely, is ever supervising serious criminal cases. It might be the case that requiring police officers to believe that the suspect is 'guilty' before proceeding with criminal investigations is the problem.
Just about every new statutory provision on criminal evidence since PACE has obliged officers to prioritise evidence indicating guilt and PACE 1984 requires that Officers need reasonable suspicion of guilt in order to justify stop and search, arrest and detention.
The open minded open minded approach suggested by paragraphs 3.4 and 5.16 Criminal Procedures and Investigations Act 1996 is at odds with the Adversarial System of Criminal Justice.
At the end of the day the police are on the prosecution team and while the is a legal obligation to look for evidence that might indicate the suspects innocence there are many practical and philosophical reasons why that might be problematic.
The inquisitorial system is better that our adversarial system in all of these respects.