Dratsab:Going back at least 4 years when I used to run briefings involving a number of different branches of council, the way it worked was the council contracted ADT Security (who operate the Parkwise brand) for warden duties. ADT are paid an agreed contract amount for this and the wardens are in turn paid by ADT.
When "caught out" by police for expired WOF/Licence label you may only get a warning, as you say, but that will depend on a number of factors. If you are ticketed and the expiry is only recent, say within a few weeks, you will generally be given a grace period (called compliance) in which to correct the problem and present evidence of its being corrected. Upon presentation of the required evidence within the required timeframe the fine will then be waived. You'll get no such joy from the council.
I don't know which council you are referring to but Wellington " contracts Tenix Solutions who subcontract Parkwise (a subsidiary of Armourguard) to monitor parking in the city.".
I see contracts and subcontracts as more clips out of the same ticket so there is less incentive to waive fines. The council does share in the fine revenue.
Wellington claims (I have no idea whether this is true)
"Council spokesman Richard MacLean said there had been a slight decline in the number of tickets issued over the past three years.
Motorists were given a month's grace period before being issued a ticket, he said.
"If the vehicle was seen on a public road during this time they would be given a caution notice as a reminder to get the vehicle legal.
"This looks like a ticket, but has no monetary penalty," he said." Dec 2012.
Other councils have grace periods. The Police are just as likely to issue a ticket that their back office refuse to waive as any council.