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
A cold night but temperatures remain above zero
Watch our report on events held to mark 'White Ribbon Day' - and access information and advice on domestic abuse and how to get help.
Outbreaks of rain will continue through the night, turning heavy in places