Uh, the car part is pretty legit though. It's by far biggest luxury expense month to month at least for me. With leasing, I'm paying almost double of what I spend in smoking which is already really bad.
So yes, getting rid of expensive luxuries is obvious first step when you're low on money.
80ish percent of the population in USA (it's 'murican article) lives in urban areas. For the 20% sure it's potentially a necessity but I really doubt it for most of the 80%
Even if the public transport is bad, it's often something you can work around on.
I'm working in a neighboring city with travel time of ~1.5 hours per direction. My preferred method is train + bicycle, it's 40min in train and rest cycling from/to train station. With car the travel time is about the same depending on the day due to the horrendous traffic during morning and afternoon.
Both travel times include taking kid to kindergarten on the way, during winter.
When you're poor enough you often don't have the luxury of working around shitty transportation and even people too poor to afford a car often end up suffering for it because of how much it can help to have reliable transportation when poor. Many jobs require having reliable transportation for example and don't count public transportation as "reliable". You need all the extra time you can get, and you need to be able to travel places on time reliably, you often can't afford to just "leave early" to make up for the possibility of your bus coming too late, or early, or not coming at all, and many poor people are poor because they suffer from chronic health complications which can limit their ability to bike or walk. In some places public transportation can also bring with it an element of danger depending on the person travelling and the place they're travelling in. On top of that if someone is so poor that they risk being homeless then a car may be their only remaining option for shelter. And having a commute that is only ~40 minutes via public transportation and bike is actually quite lucky. Not everyone manages to have that luck and it may take them hours to get to work that way when driving would only take 30 minutes, and if you work 3 jobs and have 3 kids to take care of you aren't going to want to give up that extra time. Being poor costs more than just money, it costs time and energy and mental/physical health.
It sucks that society is shaped to force many people to rely on cars but it is absolutely not a luxury for everyone.
I'm assuming you're not in the US, let me paint a picture if I may? There are zones around most major cities. Inside most city centers, you can find buses that run on 2 hour intervals (ie. Work at 9a? You'd better be at the bus stop by 6a), if you're in NY, DC, or SF maybe a subway is available but this is an largely an outlier.
Beyond the city (but still in an urban area, think row homes, townhomes, duplexes etc) are miles and miles radius of city outskirts with zero public infrastructure, if you're lucky there may be a bus line that will take you into the city directly, but those only follow the main arterial road. At this point you're going to need a car.
Finally reaching more spacious suburbs and rural areas (ranch, cottage and split level homes, lots that have a yard) which of course have no public transportation. Living in America without a car is damn near impossible.
Portland has one of the better public transport systems in the US and it took me 90m each way to my first job here, or 20m if I could get a lift. Both ways, that's losing 10% of an entire day.
Not having a car cost me 1.2 working days each week. I didn't even have a license when I moved to the US - I learned to drive at 30 y/o because its a necessity in the US.
Ah, nah. Definitely a requirement for work and not a luxury in my part of the world. Or I guess I could sell the car move into town and let metro rent prices soak up the difference.
I'm glad your living situation allows you the option to choose but my car is a necessity for me and the same goes for a LOT of people, unfortunately in today's society it's not always a "luxury" for everyone.