They already pay substantial taxes out of their income to the city they work, in most places. They already are paying for access.
You'll know they're paying their fair share when the arbitrage actually stops, but taxing non-resident earnings so aggressively to stop it produces way more negative side effects and regressive taxation effects than congestion pricing does. That's why congestion pricing is a good idea and 90% taxes on non-resident incomes is not (not to mention the ease of enforcement).
It's not "arbitrage" to commute from a place you can afford to a place you can't. Being middle class isn't an arbitrage play.
People with families aren't often willing to accept the living conditions they'd need to in order to live in NYC while paying market prices. So they arb and get suburban living conditions with urban employment.
The cost of their decision to do that is mostly borne by the respective communities (home community loses economic productivity and then city community bears increased infrastructure consumption).
We would know there's zero arbitrage when zero people did this. Which again, I don't think is the goal to shoot for. But simply asserting you have some god-given right to make this arb indefinitely at zero cost is a losing argument.
You didn’t say they should pay as much as they are willing to pay. You said they should pay.
They are paying!
Your new goal is that nobody can afford to work in the city except residents, but that is an objectively dumb idea, and certainly has nothing to do with a “fair share.”
First, in most cities people don't pay income taxes to the cities they work in but do not reside in. At least in the US this is not typical.
Second, the position that people should pay to reduce their negative externalities does not necessarily imply the view that they pay nothing today. It implies they ought to pay more.
If someone pays for entry to Disneyland, steals a t-shirt, is a valid defense that "they paid" when they bought the ticket? No, obviously not. Does demanding that they pay for the t-shirt imply that they did not pay for a ticket? No, obviously not.
Nevertheless, NYC is the only city I’m aware of in the USA that has congestion pricing, and I’m shocked to find that non-residents who work there do not pay income tax to the city. I live in OH and have to pay an income tax to the small city I work in even though I’m not a resident of said city. I thought it was more common.
I, as a realist, believe in systems with flex. As our very own patio11 put it: the optimal amount of fraud is nonzero. Here, the optimal amount of unfairness is nonzero. Or stated another way: the cost of eliminating all unfairness would not be worth it.
The assumptive jumps are not necessary here!
So now I’m honestly asking, are you or are you not arguing that the general goal is to end people "not paying their fair share” (which you equate to living outside of the city you work in)?
Also can you please explain why you believe that “fair” is measurable in this way? Can you give another example of something where a common person would use a similar definition of fair? I think that your definition of fair means stores without dynamic pricing are unfair, which seems crazy to me.