The vast majority of this traffic is from Manhattan - otherwise it wouldn't be spread across so many routes. If you want to designate a cars-ok route in Manhattan between the Battery Tunnel (to Brooklyn) and the Holland Tunnel and let that back up, you could do that and it would be less of a mess than the status quo: it would stay on West Side Highway out of the way and it would have less traffic.
One time I took a taxi from Newark to my home in Brooklyn, and the taxi driver dropped me off right after getting out of the Holland Tunnel (next to a subway stop) saying he didn't want to deal with more traffic. There is no effective vehicular link between New Jersey and Brooklyn right now. There is a moderately effective link between each of those and Manhattan, that's it.
Your take seems rather shallow. Accessible infrastructure includes curb cuts (originally designed for wheelchairs, also make sidewalks useable by the elderly, strollers, etc who have issues with a 6" step), audible crossing signals (meant for visually impaired, also alert those who are looking at their phones), bike lanes (meant for cyclists, improve the conditions for pedestrians and residents too), .... The list goes on and on where minor improvements in infrastructure design create massive improvements in public spaces.
I'm raising this in the context of the elimination of cars. The current infrastructure pushes a lot of people into taxis. So if you eliminate cars you either have to expand accommodations or just declare the island inhospitable to anyone that doesn't pass a fitness test.
You can support effectively restricting the wealthiest hub of our largest city to just people who are like you and in your life situation, but it's not going to be a widely held position.
This should have been impossible, and I should have been forced to leave my car where it was, take a bus to St. George, and get on the ferry.
Everyone gushes about how awesome transit is, but that’s only true for a few areas of Manhattan and Brooklyn. If you need to take a trip that isn’t in the happy path, a car is way better.
I’m just loosely estimating here but $50/day for vehicle storage seems like about what I would expect it to cost based on other land use in Manhattan. But of course none of it would be possible without a massive subsidy in the form of public road access.
My taxi story is an anecdote, sure, but it goes to show there isn't reliable NJ/Brooklyn transportation via Manhattan streets. If I had been going towards the airport I would have missed my flight. Or put another way - right now on Google Maps, getting from where I am in Brooklyn to EWR would be faster via Staten Island than via Manhattan. If the argument is that X is reliable, examples of X being unreliable once in a while are in fact evidence against it and not just anecdotes.
That only works well if your origin or destination is in Manhattan. To go from Union City NJ to Belmont Park on a weekend is a 45 minute drive or > 90 minutes on transit consisting of bus, subway, LIRR, another bus.
There are similar examples even within NYC, like Red Hook to Jackson Heights.