The downside is that you're failing to do the thing you set out to do. In theory the rich person (say $1,000,000 in income) places a high value on their time, so you impose a higher fine on them (say $20,000) to try to deter them. But the Uber driver only makes $20,000 total, so the fine for them is only $400. Meanwhile a middle class person making $50,000 pays $1000 -- 2.5X what the rich person incurs (assuming the fine the Uber driver pays is amortized over the fares).
> Do you have a better example?
Name basically anything that incurs a fine. A rich person who wants to do it and is "deterred" by the high fine just hires a poor person to do it for them. This is often what they do anyway because it saves them the labor independent of lowering the fine.
> I doubt people driving as a business are all that eager to lose their license.
But that has nothing to do with the fine, it's a separate penalty which doesn't exist in most other categories, apparently isn't sufficient (everybody speeds anyway), and the incentives of the driver and passenger are already aligned. They both want to get there faster, the passenger to save time, the driver so they can get another fare sooner.