Macnamir centred on the death of American mathematician Scott Johnson in 1989 at a Sydney gay beat, for which Scott Phillip White was sentenced three weeks ago to nine years in jail after admitting to manslaughter.

But barrister Mark Tedeschi on Friday instead argued evidence regarding Macnamir was irrelevant to the inquiry.

Any material regarding former NSW Police deputy commissioner Michael Willing and detective Pamela Young, who were both involved in the investigation, was also argued to be irrelevant.

He said homicide investigations were being used in the inquiry to suggest police had a "grand conspiracy" against LGBTQI people.

"The inquiry could come to the conclusion that there was an attempt by a team of police officers to understate the incidence of gay hate crimes," Mr Tedeschi said.

"(The investigations) could be accumulated together to come to the conclusion that there was - what I would loosely categorise - a grand conspiracy on the part of a very large number of police officers to do the same."

It is unclear when the inquiry will resolve the issue raised by police.

A 13th block of hearings - on the investigative practices of the police force - will start next Tuesday.

During the December hearings, police also took issue with the relevance of some material before the inquiry and the resources needed for the probe.

A letter claimed the inquiry's orders meant about a dozen investigations and reviews by the unsolved homicide team had been delayed.

The inquiry's commissioner, Justice John Sackar, dismissed the claim at the time as a "misguided and misconceived" assertion and "offensive" to the special inquiry.

The inquiry into LGBTQI hate crimes has been examining the unsolved deaths of 88 gay men between 1970 and 2010.

Justice Sackar will deliver a final report in August.

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