If you were that rich wouldn't you just hire someone to drive well for you? But if you liked driving for the sake of it would it not be part of the enjoyment to learn to handle different vehicles well?
Unless you had reached a level where you were having almost everything in your life managed by assistants, and you were the type of person that wanted to give up all that control, then have “your car” ready to go whichever house you were at would be the lower mental overhead solution.
I can readily believe this does happen at the right level of wealth, but there's something deeply absurd and humorous about someone sending a vanguard to their second or third home before they arrive.
My very typical American suburban home on a 0.2 acre lot is better built, has better views, parking, heating, cooling and so on than a 3 generation rich (from my standards) cousins' home in India. However they do have half a dozen servants at home and I have obviously none here.
So it does sound weird that people seek even further from developed world middle class point of view.
Most people don't really like it, but find it to be the best option to go from A to B quickly. If you involve other people, be a driver or a renting business, you add complication and cost.