Hamilton Mayor Julie Hardaker also apologised for the "unnecessary" blunder, which had damaged the council's reputation.
Mr Macpherson said the "debacle" showed Ms Hardaker's new governance-focused structure was not working and the council could not leave it all to management.
He wanted to reinstate the "checks and balances" of the previous structure where there were more committees and sub-committees.
"Hamilton City Council's elected members have been focusing so much on a 'pure' governance model taken from the pages of the corporate structure handbook that we have forgotten that we live in the real world where staff and management do not know everything."
Angela O'Leary said the current system was "rubbish" as things were left up to the chief executive, and councillors were brought in only to clean up the mess.
"I am sick and tired of being told to 'stay out of the kitchen'. It was working perfectly fine before and it isn't now."
Mr Wilson also supported his colleagues and suggested the council follow a portfolio-type model where each councillor had responsibility for areas of interest, passion and expertise.
He wanted to take back the power from the "inexperienced" mayor and "recently arrived management bureaucrats".
The council tried a more portfolio-style format in its first nine months of the new council.
However, following a review of the structure in June, Mayor Hardaker introduced a more simplified structure which she said would improve governance, set policy and improve decision-making. It is this structure the three councillors have slammed.
Ms Hardaker could not be reached for comment but in a statement on Tuesday defended the structure and "governance-focused" approach.
She rejected any suggestions the latest "communications stuff-up" was a result of this more governance-focused approach and instead blamed staff for not having an awareness of the impact their work had on ratepayers.
"So in the interests of common sense and good governance let's get back to reality and deal with the issue properly."
Councillor Pippa Mahood, who has been leading the council's district plan review, disagreed councillors should be "in the kitchen", but said they did need to be reassured the council was doing the right job.
She said "floodgate" was caused by staff being too busy and failing to brief councillors on the communication strategy for the district plan review.
"Sometimes they forget they have the public they have to work for," Ms Mahood said.
FLOODGATE
* 28,000 residents were sent letters telling them their properties were at risk of flooding.
* This has caused worry as some residents fear it will have a negative effect on their properties.
* The council has stopped the process and apologised for the blunder.
