Councillor Mike Lee questioned the value of the review.
"They seem to want to repeal the special legislation for the Auckland War Memorial Museum and ... for Motat and stick everything together in one big corporate entity, which I don't think is going to be helpful for our cultural heritage at all.
"It would be quite dangerous for the ... memorial museum that the intention is to have a Super City-like, amalgamate-everything, bigger-is-better - and we know from the Super City experience, it isn't."
Lee said changes were needed in some of the institutions, to make them focus more on aspects of New Zealand heritage that they seemed to have forgotten, such as Auckland's harbour ferries. But he feared the review would simply foist more corporate culture on the organisations.
The review's stated aims are to see if more "value" can be extracted, whether spending priorities should be changed, and whether the organisations should be run differently.
Mayor Phil Goff has called for a better governance system but told the organisations the review was not about cutting costs.
There are concerns in the council over effectively having to hand over what the memorial museum at the Auckland Domain and Motat in Western Springs demand, without having corresponding control over the spending.
This is because these two museums, under their statutes, get to charge a levy. The council has this year agreed to the funding demands.
"Disputing the levy quantum and entering arbitration is the alternative, but this is not recommended," officials overseen by financial chief Sue Tindal told councillors when they considered the memorial museum's levy of $30.735 million for this year, which is 3 per cent more than last year.
"Enhancements to the wider governance and funding arrangements for Auckland museums is a longer-term goal and this will be best achieved through consensus with the institutions.
"In recent years the museum has used its legislation to levy council for significant increases in funding, without necessarily being clear in its accountability documents as to how this money is being spent and what value it is delivering for Auckland.
"Council is in the position of being unable to influence the levy and balance it against other priorities within both the sector and its overall budget."
The memorial museum receives nearly 80 per cent of its $39.1 million revenue from the council. In 2015/16, 890,500 people visited.
Its trust board chairman William Randall has expressed the museum's support for the independent review - and its strong objection to the Tindal report's criticisms.
"As population and land values have increased, the museum has maintained its levy requests in absolute terms at a nearly constant dollar level," he said in a letter to the council.
And it had made great efforts to be open and clear with the council.
The museum said that, because of the financial pressures on the council, it levied only about one-third of the maximum permitted by its legislation, down from 54 per cent a decade ago.
Of Motat's planned $18.58 million total revenue this year, $15.22 million - 82 per cent - is from the council. It had nearly 249,000 visitors in 2015/16.
Director Michael Frawley said the organisations being reviewed were already discussing how they could work together.
He had an open mind about the review. Amalgamation was one option and had some merit, he said, such as saving money on back-office functions which could be spent on improving displays. The biggest risk was around what funding mechanism would replace his museum's legislated ability to levy the council.