"I think the community sees itself as Hamilton now and it is time to move on," Mr Bunting said.
He also argued that the system did not just favour sporting and radio personalities.
"Cry me a river, I and people like Siggi and Leo have spent years investing in this community in other capacities.
"It really is a non argument saying it favours people with high profile."
Councillor Dave Macpherson said the problem with a citywide system is you end up with one ward dominating the other.
"We ended up with the River Rd syndrome, where there were 11 councillors and nine of them lived on River Rd," Mr Macpherson said.
He also said the election campaign spending cap was too high for a city wide system, and that council needed to be made more accessible.
Councillor Angela O'Leary said people are asking for a diverse council.
"They have strongly indicated to us that they are looking for more choice of candidates."
She agreed with Mr Macpherson saying the price of running in the election was putting potential candidates off.
With the two-ward system in the 2016 election, east ward candidates were allowed to spend up to $50,000 while west ward candidates were allowed to spend $40,000.
The spending limit is determined by population.
"If it was a true democratic system, wealth would not have a part when running for a democratic office."
Mayor Andrew King said the council was confident the two-ward system is still a good fit for Hamilton in 2019.
"We recognise that a number of people think an 'at large' system (no wards) might be a better fit, because they think of Hamilton as one big community and this system would give them better choice of councillors," Mr King said.
By law, the council must review its representation arrangements at least every six years.
The council will have another opportunity to review its representation arrangements in three years' time, which will coincide with a review of the electoral system (first-past-the-post vs single transferable vote).
Formal consultation on the initial proposal to retain the existing two-ward representation arrangements will open on August 24 and end on September 24.
Public hearings will take place on October 9.