Newport West MP Paul Flynn says the row over the forcing out of the former Gwent Chief Constable by the force's Police and Crime Commissioner shows "it is the system that is wrong - it's going to happen elsewhere too."
He said the problem is "two people thought they were running the police force".
Ms Napier has called on the UK government to consider whether the independence of operational policing could be compromised by the power given to PCCs.
More top news
Rain moving east, heavy at times
The Lesbian, Gay, Bisexual and Transgendered communities in Cardiff are celebrating 30 years of campaigning; as part of LGBT History Month.
Cloudy at first, with outbreaks of rain gradually easing during the morning.