There are seemingly obvious ways of countering that, such as included mandatory upper limits on ticket contest rates. Are these not part of the contract? Who enters into contracts with no provision for actually delivering the service at an acceptable level?
People focus on the dollar amounts for contesting tickets, but more likely the problem is time.
If you have a minimum wage job you likely don’t have the time flexibility to allow you to go to any kind of “court” to contest a fine. If you have a high paying job, then likely the time costs you more than what you save - especially if the cost of contesting a fine in capped at something “affordable”.
Your other question: what is “acceptable service level” measuring for a ticketing service?
That's the case for government run ticketing as well. Even if only a small percent of people contest unfair tickets, you can use that as an indicator of how many unfair tickets are being issued. If it goes up under private ticketing, and assuming you don't change the method for contesting, the odds are good that they are doing something to cause it. Hence you could write a service level agreement that says something like "Percent of issued tickets which are contested shall not vary beyond x% from y (the prior rate). Percent of successfully contested tickets will not vary beyond z%", etc.
To come up with an actual service level agreement would require some knowledge of what outcomes are desired and some thought about how those numbers could be gamed, but I don't see why this is not possible. Private companies contract out work all the time and don't seem helpless in their ability to get what they want from it. Why should the government not be able to do this?
No it's not, that's the point - a private company has a single goal: making money. It isn't in the interest of a company that gets revenue proportional to tickets issued to, for example, ensure that parking restriction signs are visible, etc.
A city obviously has _some_ incentive to get more money from tickets (in the US see things like ticket revenue requirements, "civil forfeiture"/theft, distributing the received assets to the orgs issuing the tickets, stealing property, etc). But the city also has actual non-revenue reasons as well - for example I have received multiple parking tickets around my house over the last few years because there are parking restrictions to allow street cleaning, etc (the problem isn't the signage, it's the forgetting about the restrictions, and them being "2nd and 4th Tuesday" on one side of the street and "1st and 3rd Tuesday" on the other).
Similarly traffic tickets say are intended to make roads safer by discouraging speeding, etc (although they functionally just mean speeding is allowed if you are rich).
Using speeding tickets as an example, it is in the interests of an organization that receives revenue from tickets that people do speed. On the other side various governments have a real interest in not having crashes, etc as that has impact on the economy, it impacts voters, etc. But even this depends on the people enforcing traffic laws not being corrupt - and gov agencies getting any funding from tickets creates an obvious moral hazard. In California at least you get the CHP getting significant funding from ticket/fine revenue, and as a result of this the CHP does not maintain visibility while speed checking, but instead hides. The former results in people not speeding, the latter means that they get to issue tickets.
An illogical extreme of this would be to set the speed limit for a freeway below the design speed for said freeway - this is a particularly subtle one: most research shows that people will tend towards driving at the designed speed of a roadway, so you can create an environment where the default behavior is "breaking the law" giving you a limitless source of income. Honestly, it's why things like speeding tickets, etc should be required to have all fines sent to a separate account (say victim support or something) where the relevant agencies can't use the income directly or indirectly.
This is why the incredibly hated traffic cameras are infinitely superior to manual speed checking - fixed cameras in locations where speeding is dangerous are, well, fixed. This means that even if people do speed, they learn to avoid speeding in places it's particularly dangerous, if only to avoid guaranteed tickets.
And what are the incentives of the people in the government agency? You seem to assume that absent financial incentives they will behave altruistically. I would argue that part of the reason agencies have those financial incentives is to give them a reason to perform that task at all. Government employees are not a cadre of uniformly civic minded people. Just like everyone else, they tend to seek to maximize their own benefit. Without financial incentive, it can be other motives, like the desire for power or to avoid work.
As an example, a friend of mine was engaged to a fellow who worked as a mailman in New York. His mail route took him 2 hours to complete, but officially it took him all day. After he completed his mail route, he'd go to the gym, run errands, etc, then show up at the end of the day to clock out. Apparently he was far from alone in this. The mail routes had been established long before and were passed on from carrier to carrier, none challenging the fiction that gave them so much free time. Their supervisors must have been aware of this given how long it had been going on, but apparently they had no incentive to interfere.
Another example: there was a precinct in the Bronx many years ago where the police would fulfill their parking ticket quota by going down a block and issuing tickets to every car, regardless of meter state. People who lived in the area were aware of this and regularly contested the tickets. Eventually someone noticed that the contest rate was extremely high and almost always successful and they got in trouble. They apparently felt no incentive to ensure that their ticketing raised revenue for the city or encouraged meter use. Their sole motive was meeting the quota.
I could list many other examples of where government employees, without incentives to do their job, did them poorly or not at all. High profile ones like the police are actually more accountable than many of the smaller agencies. In my experience it's not unusual to find yourself waiting for days for a person to sign a piece of paper which is sitting on their desk. Clearly that person is not being evaluated on whether your needs get attention and no other motive is at play. But this is actually one of the more successful outcomes. In many places, bribery is necessary to get people to do their job.
In short, incentives are always a problem, public or private. In order to get things done well, it is necessary that incentives are constructed properly. That takes effort and instances of failure to do it properly abound for both public and private institutions.
