Gas taxes (partially) pay for the roads. Get rid of those and you've just decreased your tax base, which means you're going to have to pay for it from another tax. It's just shifting the tax burden. We can argue about what's a better tax policy, if a certain tax is progressive or regressive and so on but wherever the money comes, somebody needs to pay for the roads.
NYC is one of about 2 places in the US that actually has usable public transit, barring certain outer boroughs where car ownership dominates. It's largely a hub and spoke model though so it's good for going into and out of Manhattan but not so good for, say, getting from Red Hook to Flushing so driving will dominate that kind of travel.
But that's why congestion pricing is targeted at Lower Manhattan and can't really spread beyond it. Like see how far you get trying congestion pricing in Houston or Dallas, let alone Bakersfield, Boise or Lexington (KY).
Economic incentives work. They're probably most responsible for the drop in smoking. Congestion pricing consistently changes people's behavior and every metric shows it. Some bus lines in NYC now move nearly 30% faster.
I don't know what island you're talking about and what happened but will generally agree that people are struggling all over. It's well-known that real wages have largely been stagnant for 40-50 years.
But that's not a problem caused by gas taxes. It's caused by capitalism.