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The solution to fines is to simply get rid of fines and instead use a more aggressive "point" system.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.