But that makes people no longer equal in the eyes of the law. A better solution to that problem is to make sure there's some non-monetary component to the punishment too, e.g., towing the car, which then takes time and inconvenience to retrieve, or community service for worse things than parking tickets.
Why would a percentage based fine make people unequal in the eyes of the law? The percentage does not change and everyone would feel the punishment in the same fashion
If a baby were to punch another baby, the second baby would feel pain but if that same baby were to punch a full grown 94kg man, the man would feel nothing. So we scale up the situation appropriately to two 94kg men.
From my perspective, having a small fine only hurts people who are poor where that is not even thought of as a punishment of even an inconvenience for the rich.
But it does, the idea of the fine (or any punishment) is to stop you (and others) from doing that again. The equality is in what you are and are not allowed to do and in how harsh the penalty is to you.
Well then update the law to better refer to what equality is. x% of your wealth + y% of what you could earn this year is far more equal than a set number