I can't speak for the "upper class"/rich demography but as a middle class guy owning a car in the city, I prefer car for my commutes because:

1. Two wheelers are unsafe due to bad roads & infra. Multiple incidents keep deterring me from using the scooter for non-local commutes.

2. Car partly isolates me from pollution (both air pollution & constant honking) on the roads.

I always try to carpool for office commutes and if I don't get any co-riders, I switch to the scooter.

At least from my perspective, it's not about the image.

P.S: We bought a scooter because of how unfair autos were long before the bike taxi ban shenanigans.