In many ways, a congested city works like a income-adjusted congestion tax, where you pay with your time. Since the time of rich people is more valuable, the burden seems "fair". The only problem is that the time is wasted, no tax is collected.
Maybe we should accept that political reality and setup income adjusted congestion taxes, putting the revenue to work to ease congestion for everybody.
Another option is to disburse a limited, equal number of "tradable driving hours" to each citizen regardless of income. You now have a market that eficiently allocates the limited public resource, allowing poor or thrifty citizens to earn tax credits, while allowing rich drivers to pay a fixed rate for each driving hour exceeding their allocation.
It's good politics, bad economics - but still much better than wasting millions of man hours each day.