No one is actually answering why its a big fantasy among certain groups as opposed to other arbitrary and random groups, which is a huge shame.

1) Left is culturally dominant (the establishment) at this time, therefore all social signalling (social media) is left wing and has a single progressive unified outlook on life. Even if "emperor has no clothes" style no one actually believes it. That has two effects. One is that someone started it so everyone has to parrot it as common sense and the only socially acceptable outlook because there must be only one correct answer to social questions. The other effect is due to only one outlook being acceptable, any random people MUST be compatible with any other random person. In the real world of course you can't just randomly shove ethnic, cultural, or religious groups that are unfriendly with each other into the same very close shared personal space. It would be badthink apostasy to think everyone in shared cabs will do anything other than hold hands and sing girl scout friendship songs. In the real world of course it would be hell.

2) There is a cultural superiority complex or rationalization or something that drives them as a group against scheduled activities. The famous "look at all those residential driveways full of cars" is a tired trope. Its a little short sighted in that 99.99% of my life I have not required the services of an ambulance therefore I don't want or need ambulance service in my community. The majority of the car buying public has an elementary school daughter who gets out of school at 3:40pm not "when she can get an uber" or "school children should be able to participate in contracts" or whatever. It doesn't matter if on a 24 hour average all the cars at school pickup are empty 95% of the time therefore we only need 5% the number of cars... doesn't work that way, we need 100% of the cars that are lined up at pickup time. Ditto 9-5 office salaryman work or sports teams or anything with a fixed schedule. Sharing only works if everyone in your culture never looks at a clock and just hops bars when they feel the need, not 9-5 at the ole salt mine. Living according to a clock is extremely right wing. Most phones spend most time in pockets therefore we should share phones. Most underwear spends most of its time in dresser drawers therefore we need an uber for underpants.

3) I believe there's some residual "workers of the world unite" and we shouldn't own property and maybe the state could own all the cars just like the state owns all the bus vehicles and passenger trains. How dare the proles have agency and have the capability to move without government cooperation and tracking, etc. Much like owning a gun is fundamentally immoral because we should trust Big Brother to protect us at all times and any implication Big Brother is not our friend is badthink of the highest order therefore gun ownership is badthink. I'm sure Big Brother's cars will only have our happiness as their sole priority, it would be wrongthink to consider otherwise.

4) There is a study I don't have a link to WRT disgust reflex along political spectra, to the extent that sitting next to a smelly creepy homeless guy is likely to make a right winger retch and get disgusted at the smell but a leftie is physically more likely to ignore it while celebrating the vibrant diversity of the situation. Its like how urban people literally don't mind crime as much as suburban or rural people, although there's self selection going on there.

5) There are known demographic issues WRT ownership of a childs car seat correlating with various political outlooks etc. Inherently there will be less interest by left wing people in car ownership.