You're assuming the problem that fines address is modifying driver behaviour. It isn't. The primary problem fines address is revenue.
Anecdote time: a friend from one of the nation's major universities was involved in a road authority funded study to evaluate the safety impact of newly installed speed cameras at several intersections.
They found there was none. Said road authority pulled the plug and pretended like the study never existed after that.
This distinction is made very clear, for example in a parliament answer by the justice minister: "...it is clear that the purpose of fines is not to increase the revenue of police departments but first and foremost to deter traffic violations and increase traffic safety."
You're contradicting your own claim.
Just because someone in a PR position says the purpose is not to increase revenue doesn't make it so. It doesn't matter where the revenue goes, the fines generate revenue. If they didn't care about revenue, they'd use penalty points - with the added benefit of not fucking over the lower and middle classes.
Just for fun, I calculated this fraction for a given year. The revenue from all traffic violation fines accounted for a whopping 0.1% of the total state revenue.
So apparently the only purpose of these traffic fines are to raise the state revenue by 0.1%, despite the explicit stated purpose of the legislation and any evidence to the contrary. Does that make sense to you?
Is this one of those things where you just know you're right because you feel it in your gut and nothing can ever convince you otherwise?
That will be the case with any effective punishment. You can be sure they'll fight points just as hard. Ofc still way better than a flat fine.
The points system disproportionately advantages the working poor. Speaking from experience, we have a mixed points+fines[1] system in Poland.
A wealthy person can easily weasel his way out of the points by either having a lawyer argue in court, or - especially in case of automated enforcement like speed traps - simply pay a third party (usually poor person who drives little or not at all) to accept the blame & penalty points in his stead by formally admitting to having been driving during the infraction. I've seen many ads for such exchanges.
Since several kind of jobs directly depend on being able to drive, the law customarily provides a way to shed the points in an expedited way. Typically it involves taking part in road safety courses and/or extra examination. You pay, you attend - or not, if you pay a little extra on the side - and your points get cancelled out. This is much more doable for somebody with expendable income and ability to shuffle work schedule around.
Absent such ability to shed or cancel out the penalty points, any working poor or middle class person who depends on ability to drive to earn the keep is under constant threat of loosing the job. Not a good position to negotiate with the employer.
tl;dr: The points system is unfairly burdensome for the working poor due to the system being much influenced by money. All the points do is to hide away the fact that money gets shit done.
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[1] the fine are fixed, and rather mild from middle class' perspective.
The solution to fines is to simply get rid of fines and instead use a more aggressive "point" system. I'm not wealthy by any means but the threat of a $200 ticket has zero impact on my driving habits whereas the threat of having my license suspended if I get 2 tickets in a 12 month span (a hypothetical example of possible punishment btw) would definitely change how I drive.
I can't really think of any crime that carries a fine rather than revocation of certain rights where this wouldn't work. The only issue is that of enforcement, you have to make the threat of getting caught a second or third time real enough that the punishment becomes psychologically meaningful.