Lets focus on non-necessity acts here (e. g. traffic violations).
Deterring people is not the only goal, it also needs to be fair/appropriate. And this is where, IMO, the income-adjusted fines fail.
Fines should be adjusted depending on the offense commited, possibly also taking into account the intentions. Personal wealth is not a factor that seems reasonable to me to take into account regarding the fairness.
Essentially, I believe that everybody should be treated equally before the law. Nobody should be treated better or worse (or have a better or worse punishment) just because of their social status. That’s why I believe that fixed fines are fair and the suggested varying punishments are not. I do recognize that they may deter wealthier people less.