Parking is a service that you receive in exchange for money. Our society has accepted that those who have more money are able to purchase more goods and services.

Fines are not payment for services rendered, but a deterrent for behavior we don't want anyone to engage in. If it doesn't scale, then it's only a deterrent for those who can't afford it.

That is effectively the case. Taxes, in theory, scale with income and a lot of the car infrastructure is tax subsidized including street parking.

Yes you probably could but taxes, that are already proportional, will cover most of the cost of the parking.