I agree with your last line, but the rest not so much - Yes, the monopoly on violence exists, but the idea that one must always consider that the state will kill people on the introduction of a simple fine is just silly.
Looking at the monopoly on violence as the backing to the entire system of law? Sure, it's absolutely there. It's something to consider when discussing the merits of the existence of the state at all.
But within the context of the state already existing, looking at the introduction of an individual rule that may result in a fine through the lens of "is this worth someone's life" is nonsensical - it's just not going to cost anyone's life, it's not a reasonable thing to consider. Especially outside of countries where law enforcement are routinely armed and trigger-happy - there is no reasonable pathway to a fine costing lives. What we do see is fines just going unpaid if they can't be recovered by administrative means.
It is notable that in both your and the GPs timelines, the other party turns to violence first. Your line -
> What if the bank tries to stop you doing that? Then you send in armed police.
really seems only to apply in places like the US where you have a bigger problem with police killings and a societal leaning towards firearms and escalation of violence. The UK (for example) will only send in armed police as a response to situations in which the other party is also armed and a credible threat to lives, they won't just start shooting.
tl;dr - considering the consequences of complete societal breakdown as part of your scenario when deciding to introduce a new type of parking fine is... well it's fricken hilarious really.
As Dennis from Monty Python and the Holy Grail would say, "come and see the violence inherent in the system!"
The thinking is rooted in exploring the full breadth of coercions available to the state, with both actual and implied violence.
Of course it's vastly more likely a person who has been fined will pay the fine, or the other entities which he relies on for money (his employer, his bank) will extract it from his assets, or if he has no such assets, the state will start to go after his personally-held assets. As you know, the UK has safeguards, the state can't sieze your residence to make you pay a fine, but they can sieze second homes, or more relevant to this discussion, your car -- if they don't judge it essential for your livelyhood. The UK state isn't looking to reintroduce debtors' prisons, they prefer to keep a wrongdoer economically active, provided they don't think it'll lead to further harms; so in the case of someone fined to buggery, and banned from driving (let's imagine not just parking fines but persistent reckless driving), and could technically walk or get the bus to work, the state may well sieze the car and auction it.
But then if the criminal tries to keep the forfeited car locked up, the state then authorises its burglary, and we can then keep upping the ante between the unstoppable force and immovable object; does the state give up trying to sieze the car (and thus not enact justice; the criminal ultimately did not pay his fine), or does it proceed? And if it proceeds, what can the criminal do to prevent it, that is "non-violent"? If baliffs turn up at his door with a warrant to seize the vehicle, do they just go away, empty-handed, if he politely says no? Or do they smash down the door and ransack the place looking for the keys? Do they wrench open the garage door and lift the car out? If they do that, are they being violent yet? If the man tries to resist the baliffs searching his abode for car keys, is that violent yet? If they then try to stop him resisting (e.g. by having authorised police attempt to restraint him, without using weapons), is that violent yet? If he arms himself in order to resist being restrained to resist having his car siezed, are we now at the point of violence, even if he doesn't need to use the arms? And so we can go on, action and counter-action, there is always a further escalation available, and it will, at some point, reach violence. You can't have a state that insists on a course of action and a citizen who insists on rejecting that course of action. Someone has to prevail. It is almost always the state.
The cases we see where the state doesn't prevail look like Mexico vs drug gangs, or Lebanon vs Hezbollah. Places where armed paramilitary organisations are the de-facto government. That's the sort of place where, say, a Hezbollah fighter could get a parking fine, and the government would ultimately not collect and the criminal can lead a happy life, because he has a whole set of organisations (including employer and bank) who lead an armed resistance against the state, and are more powerful than the state, so they prevail.
Looking at the monopoly on violence as the backing to the entire system of law? Sure, it's absolutely there. It's something to consider when discussing the merits of the existence of the state at all.
But within the context of the state already existing, looking at the introduction of an individual rule that may result in a fine through the lens of "is this worth someone's life" is nonsensical - it's just not going to cost anyone's life, it's not a reasonable thing to consider. Especially outside of countries where law enforcement are routinely armed and trigger-happy - there is no reasonable pathway to a fine costing lives. What we do see is fines just going unpaid if they can't be recovered by administrative means.
It is notable that in both your and the GPs timelines, the other party turns to violence first. Your line -
> What if the bank tries to stop you doing that? Then you send in armed police.
really seems only to apply in places like the US where you have a bigger problem with police killings and a societal leaning towards firearms and escalation of violence. The UK (for example) will only send in armed police as a response to situations in which the other party is also armed and a credible threat to lives, they won't just start shooting.
tl;dr - considering the consequences of complete societal breakdown as part of your scenario when deciding to introduce a new type of parking fine is... well it's fricken hilarious really.