No, the scarce good is right-of-way on such-and-such road, at that time of day. You presuppose the existence and maintenance of the road, which is of course an error.
So how do roads exist and persist to be "distributed" in the first place? Taxes are collected to pay for this. It's too complicated for me to unravel how/which taxes exactly pay for the roads exactly, but let's say you can more or less identify the road-maintenace funds with a generic gasoline-tax that's collected (I doubt this, but it's the best approximation I can think of). Thus, the way we currently "distribute" right-of-way on whatever-road is,
(a) we collect a tax on people in proportion to the distance they drive so as to build and maintain the road, and
(b) we allow them to use roads (or queue up for using roads) on a first-come, first-served basis.
You are claiming that it would be fairer to replace (b) by a rule
(b) if the road is designated high-use, charge a fee to queue up (in a queue that is therefore shorter, or nonexistent) for using it.
Your total method of right-of-way-on-roads distribution, then, would be to charge people a total tax of the form
A x D + B x C.
where A = the gasoline-tax, D = the Distance people drive, and B = the "congestion-pricing" fee, and C = the distance people drive on the Congested (high-use) roads.
It's unclear to me why this is fairer than the tax we currently use, which is
A x D + queueing
Obviously this depends on how one defines "fairness". Many people would identify "fairness" with the impacts on people of various wealth levels. Let's look at that.
It seems probable that your congestion tax B x C is a regressive tax (added to the tax A x D which was already arguably regressive). That is, as a percentage of peoples' income (or of their wealth), it decreases. After all, extremely wealthy people won't feel the bite at all.
Meanwhile the "queuing" tax implied by simply allowing free use of roads (and people then wait in traffic), which is a tax on peoples' time, is perfectly flat: a one-hour traffic jam takes up 1 hour of a rich person and of a poor person's time; that time is far more valuable to the rich person so he's "paying" in proportion to his income, roughly speaking.
So, your definition of "fairness" really can't be the one that identifies "more progressive" with "more fair" and vice versa.
Another definition of fairness I can think of is based on a different sort of consideration: since we are dealing with a government action and government coercion, something is fair of the coercion is in accord with the implied social contract that gives the government its ongoing authority. In this case, we have a government that has been
(a) collecting taxes from people for decades,
(b) to use them (in part) for roads,
(c) with the implied promise that the roads are equally accessible to rich and to poor who have paid those taxes.
So I say it would be unfair to, having done that, change the rules of the game and turn around and restrict the roads that were already built with the previous tax money collected under conditions of promise (c) and change the terms of their accessibility.
But you say it's fair, so clearly you're not using that definition of "fairness" either.
What definition of "fairness" are you using, I wonder?
Red Ken in London started this as far as I know. The consequences are yet to be understood. Though I expect when the reality of it slowly sets in, it won’t be good.
My definition of “fairness” is “free exchange of goods and services.” The limited commodity is not the road, but the access during certain times of the day.
Under a queue, no one has the opportunity to exchange other goods for the good in question. I can’t say “I will go mow someone’s lawn for an hour in exchange for the chance not to be sitting in traffic for hour.” Under the queue system, the exchange is prohibited. Under congestion pricing, if someone pays me $10 for mowing the lawn, I can use that money to pay the toll and thereby avoid the traffic.
The main counterargument to congestion pricing is that it “hurts the poor.” The truth is that the poor would benefit in most cases. Many of the poor can’t afford a car and have to take a bus. Presumably, buses would be exempt from congestion pricing, so the poor who have to take the bus would save an hour of their time.
The lower middle class who prefer to drive their own cars could make their costs minimal by carpooling. By dividing the cost four or more ways, they can save an hour of their time. If four people get in a car and save an hour in traffic and pay $2.50 each, they could then get to their destination and work an extra hour. Even if they only made minimum wage, they would be better off.
A x D + queueing
Obviously this depends on how one defines "fairness".
The point isn't fairness. The point is that the road becomes more useful.
What we have is a classic tragedy of the commons situation. The road is "free". So everyone rushes to use it. Its usefulness is reduced in the sense that people spend much of their time using the road as simply a waiting area while sitting in traffic instead getting full value from it by moving along it.
Congestion pricing works by restricting access to the point where traffic continues to flow, making the road less for waiting and more for travel, while simultaneously forcing people to make a decision about whether their use of the road is really that important. So long as the road appears "free", there will be people casually using the road, creating more traffic, and forcing others that might take better advantage of the road, to wait.
Your analysis ignores the value of the road as a function congestion.
But even looking at the road strictly from a taxing standpoint, it isn't obvious that people will pay more overall in taxes or that it's even bad if they do.
If congestion taxes are used to subsidize road spending and repair, while keeping road taxes revenue neutral, then taxes on gasoline can be made lower. In effect congestion pricing allows some people to trade away their right to access by enjoying a lower tax on gas. They in effect sell their access to someone more willing to pay.
Secondly, congestion pricing opens up the possibility that people will pay more simply because traffic is reduced. They may pay the government more in taxes, but get to enjoy a less crowded and more useful road.