A union is worried that MIQ is a difficult place to speak up when workers see something wrong.
Each hotel now has its own health and safety committee, with 130 workers across the country selected as representatives in January and most meeting for the first time in April.
However, Unite spokesperson John Crocker said his union has been asking for more of a "worker voice" for months, with avoidable health and safety problems in the meantime such as breaches, staff shortages and missed tests.
"There is a disappointment that it's taken too long," he said.
"We've seen problems, we've seen breaches, we've seen conduct that the public and the media have called into question. We think, had we had thorough worker engagement, then we could have ironed some of those out along the way."
If MIQ workers see something amiss, the Ministry of Business, Innovation and Employment suggests they go to their manager or supervisor, or their hotel's operations and security manager.
It noted many of the organisations involved in MIQ already have their own health and safety committees, and said it has recently appointed Operations and Security Managers at each hotel.
However, Crocker said that hasn't been enough - workers have still failed to get the attention of management about communal areas that aren't separated, and shortages of PPE.
He said not everyone feels comfortable talking to their manager about problems, so it's vital they can shoulder-tap fellow workers.
"We hope it facilitates real engagement with the workers. They're the ones doing the work. They're the ones seeing the risks. They're actually the eyes and ears of these organisations. So not having them as part of this process was, I think, a bad call from the Government a long time ago," he said.
Employment lawyer Barbara Buckett said organisations aren't obligated to have health and safety representatives and committees if workers haven't asked for them, or if they have other channels for staff to give feedback.
But she said many of them do anyway.
Buckett said MIQ hotels have hundreds of workers and are "high-risk" workplaces so it seemed late to have just appointed representatives.
"It did surprise me. I thought that was quite obvious. I think I'd agree with the unions that it probably is a rather belated effort to take health and safety seriously," she said.
Unable to get through to senior staff, some desperate MIQ workers have taken their frustrations around staff shortages anonymously to journalists.
That's despite strict rules at all public sector agencies about which staff are authorised to speak to the media, and the protocols they need to follow.
Some MIQ workers who have engaged with the media have been sanctioned and Crocker said others have been pulled into meetings designed to "intimidate" and censure them.
He didn't think that was constructive, because health and safety issues at MIQ put the public at risk.
Associate professor of journalism at Massey University, James Hollings, said the "silencing regimes" restricting employees are becoming far too common.
He said recent whistleblower laws had failed to give them enough protection.
Hollings believed employees should be free to speak to the media about their employer, even if it reflects badly on the company.
"Of course we should be allowed to bring our employers into disrepute and criticise what we think are dangerous or unsafe practices. But they should be able to speak out about things that are wrong or which are in the public interest," he said.
The Ministry of Business Innovation and Employment said none of its MIQ employees have lost their jobs for speaking to media.
The health and safety committees will meet monthly, and all representatives will go to training courses paid for by the Government.