Peak and especially distance based pricing are fundamentally regressive and unjust tax schemes that penalize the poor. Subway fares are already regressive in that they represent a larger share of income in poorer people than in the rich, making it distance based so that people who can't afford to live in the core are charged more makes the problem 10x worse.
It’s not an unjust or regressive tax scheme to charge more for greater service. This is incorrectly repurposing the language of taxation to the reality of transit fares.
It is certainly correct that having fixed fares across time and distance is a government subsidy which arguably may even effectively target poor riders.
The lack of a subsidy is fundamentally not the same as a tax.
But when a subsidy distorts the market to the point where it causes inefficiencies in the market, those inefficiencies can undermine the value or effectiveness of the subsidy, sometimes altogether.
I.e. lack of peek pricing causing massive ridership spikes at specific hours overloading the system and making it break down.
A theoretically better system might be one with a fixed monthly fare credit for low income riders, while also having peek pricing. This shifts demand to keep the system running more smoothly while also making transit more affordable for lower income riders.
But then, why not ask the question, if we’re giving money to low income riders, why give rebates only to low income people who ride the train? Why have a low income subsidy specifically for subway ridership versus any of a dozen other things people fundamentally need. Why micromanage to that level?
Distance pricing seems to work just fine here in Japan, although I did't dig into the data on public transit, just based on my personal experience.
Fares in Osaka or Tokyo are ~$2 per 3-4 stations from your departure point. Riding to Kyoto from downtown Osaka (40km) is ~$8 and 8 stops across two lines. The prices overall are low (IMO), and Japan has lower wage inequality than the US (IIRC).
I'm not against welfare agencies subsidizing the poor. If we are subsidizing the poor that should be from a different budget: as far as the transit system is concerned rich or poor use the same resources so the income to the transit system should be the same even if it comes from a different pot.
Just because you may have a larger income than others doesn't mean you should pay more money to equal a lower income person's cost percentage of income wise, that's unjust in itself.
It doesn't mean you shouldn't, either. There's nuance to every situation, particularly when we're discussing the means by which some people quite literally survive, vs. luxury or leisure goods and services.