If we want a shift to walking, we need to prioritize dignity

I find this assessment to be untrue. If you live within a major city in the United States, you definitely don't "require a car to get around." Philadelphia, for example, has a car ownership rate of only 70% (NYC is about 45%). I can personally attest to the practicality of a car-free lifestyle here. The city's strong bus network, extensive (if unexceptional) regional rail, acceptable subway lines and trolley service, and extremely walkable downtown mean that unless you frequently travel 25+ miles outside the city to places that specifically don't have any transit, a car is a convenience rather than a necessity.

I have found that this is the case in all American cities I've visited, including those outside the dense northeast, though there's a range of quality. CityNerd spent months living car-free in Las Vegas, a place I didn't think it was "possible" until seeing his video. It turns out you can get by fine without a car. (Millions of low-income, disabled, and elderly people in cities around the country already do!) Strictly speaking, you don't even require an automobile in most suburban areas within the vicinity of a major city. It is neither temporally nor physiologically impossible/unrealistic to get around and complete routine errands on foot or with an electric bicycle, taking transit where needed. It's just undignified. It's uncomfortable, it's not necessarily speedy, it's not normalized, and in many areas it's actively stigmatized. That's why people don't do it.

When Americans say "you can't get around without a car," they are usually factually incorrect. Except in remote outposts, you can do it. However, it's not always pleasant and it's not typically dignified. It's also not necessarily safe due to excessive car-oriented infrastructure. This is the key idea: we've gotten so used to the idea of driving everywhere that, even in major cities, the concept of living car-free or even car-lite seems literally impossible. By extension, we conflate the purported impossibility of car-free lifestyles with undignified lifestyles: we implicitly assume that those without vehicles are relegating themselves to a sad, lesser existence. Often, in places without pedestrian infrastructure or public transportation, they are! (And in such wastelands, they'd probably wish they could avoid it.) In other words, we perpetuate the notion that "if you don't have a car, it's because you have no other choice." These places don't give you "dignity" if you're not in a car. But to say that this is universal in the US is false. More importantly, this kind of defeatist attitude deflects attention from simple, solvable problems in pedestrian infrastructure. Instead of evaluating the cause of a problem as a vague and qualitative cultural issue, it's more constructive to engage with the things we can do and that we already know will work, like improving the physical design of our towns, including roadways, sidewalks, intersections, crosswalks, transit and cycling lanes, and more. Indeed, travel time is a concern, but there are many policies we can enact to alleviate that too, mostly by loosening zoning restrictions, eliminating minimum parking requirements, and encouraging transit-oriented development.

and none of them have traffic like NYC.

Every major American city has significant automobile traffic because automobiles are an inefficient way of transporting people.

New York isn't even the most congested city by many metrics. Chicago, Boston, Philadelphia, Los Angeles, Miami, Washington, Houston, San Francisco, and others all rotate around the top 10 list. You'll notice that these cities happen to be the most populous in the country. That's because in cities of more than a few thousand people, it is physically impossible to accommodate personal vehicles on roadways at a rate that avoids congestion while also maintaining a level of density that constitutes an economically sustainable city. The issue magnifies at greater scales, hence the correlation. Even sprawling Houston with its enormous stroads and ridiculous interchanges has significant traffic. You can hardly find a place more interested in automobile throughput than Texas, and yet the "traffic problem" persists. Cities are natural congestion points due to their high density relative to surrounding areas. No matter how wide you make the streets, a car-centric transportation system can't move people fast enough in a city to avoid traffic: cars are traffic. The more car infrastructure you build at the expense of other infrastructure, the less incentive people have to take alternative forms of transport (like walking), and the more traffic increases. And the more car infrastructure you build, the less money your municipality has to begin with because the maintenance required for asphalt roadways is disproportionately expensive relative to the infrastructure required for other modes. Cars destroy their own infrastructure at a rate no other method of transportation does. Then the city claims there is "no room in the budget" for pedestrian infrastructure. We have to break out of the cycle.

For this reason and others it is necessary and important to heavily shift our focus away from car-oriented development and toward people-oriented development. This ultimately starts with designing our cities, towns, and infrastructure for people first (including pedestrians and cyclists), not machines. The ideas laid out in the Strong Towns articles linked above are some simple ways that every single municipality in the country can get started. While the cultural issue you bring up is real, its existence doesn't inherently thwart or preclude the possibility of walkable towns and effective transportation systems.