The argument as to whether owning a car is a necessity or luxury kind of misses the truth, which is that there isn't a binary question. It comes down to the choices available to an individual or family. If you live in the centre or inner suburban areas of most major cities, then a combination of public transport (even long distance), walking or cycling, deliveries, occasional use of taxis and hire cars will cover your needs and will almost certainly be the cheapest option if you are single or may be even for family, if all of your employment and education destinations are well connected. For this group a car is not essential. I lived in London (around the zone 3/4 boundary) for 8 years in from my late 20s to late 30s and this was fine.
If you live in outer-suburbs or satellite towns the above may still apply, especially if you are young (expensive car insurance) and / or single and particularly if you are close to shops and travel to the centre of your city for your employment and leisure activities. This is the setting I now live in, and it was only about a year after moving in that I bought a car. I continued to commute for (rail industry) work to the centre of the nearby city by train and still do 18 years later, but now there are children to ferry to activities (particularly in winter, when the walk would be in the dark) and leisure activities that are no longer easily reached by public transport. Journeys to friends and relatives are not as seamless by public transport and much more expensive, even with a family railcard. Then there are camping and self catering holidays. The latter are basically out of the question without a car, with not just clothes but cooking gear, bedding, seats, cuddly toys etc. etc. My children can get to school one by public transport and the other walking, so we could 'get by' without a car, but would be quite limited for leisure and holiday choices.
For many people living in the same satellite town and or in outer suburbs do not work in the easily accessed city centre, but have work destinations that require a wide variety of highly dispersed orbital trips, where many of the frequent and convenient public transport trips are radial. Shift workers will generate at least some very early or very late trips - again many not well served. This will apply to many public transport workers including railway operational staff, which is why many of them describe car ownership as necessary on this forum. IN my early 20s, I did a short stint driving buses, so fell into this group, even living fairly centrally. All of my immediate colleagues in the centrally located office come by public transport and some don't have a car, but when I travel to meetings with colleagues at maintenance depots further out clearly drive, given the large number of vehicles I see parked there.
All the above is before you actually get to country towns and genuinely rural areas, where public transport might just be a very infrequent bus service and a railway station several miles away.
It is pedantically correct to say that we could all chose to be in the first group or accept the limitations of being in the second group without a car - in so much as we could in theory move (say) from rural Wiltshire to somewhere in London's zone 3). However, one of the key features of this forum that must unite most of its members and visitors is that they either work on or have a keen interest the railways or both (and probably much of the rest of public transport). Many of them will even get some kind of discounted travel. And even here there are a fair number of people who acknowledge that their main life style choices (and not just extravagant treats) would not be viable without car ownership. This is despite that car ownership being a non-trivial cost, for me around £1,750 per year over 10 years for all costs including depreciation except insurance for around 6,000 annual miles in a now 15 year old car. This is about as cheap as you can do it and young driver's insurance could be almost as much again, so it isn't a surprise that younger people are more likely to find that living without a car remains their economically rational choice. I have been on both sides of this question...