It makes it easier for the driver/chauffeur to get out and open the passenger's (rear, driver-side) door.

That may be true, but it's not quite that.

In Savoy Court, vehicles are required to drive on the right. This is said to date from the days of the hackney carriage when a cab driver would reach his arm out of the driver's door window to open the passenger's door (which opened backwards and had the handle at the front), without having to get out of the cab himself. Additionally, the hotel entrance's small roundabout meant that vehicles needed a turning circle of 25 feet (7.6 m) to navigate it. This is still the legally required turning circle for all London cabs.[1]

[1] https://en.wikipedia.org/wiki/Savoy_Hotel#Savoy_Court

Hackney carriages still exist. And a great deal of them made the move to electric. That's just another name for car for hire or taxi.

That was a til for me too, i though that means the shape of the vehicle.

> That's just another name for car for hire or taxi.

There's a legal distinction between taxis and hackneys. Taxis can be taken from a taxi rank or flagged down, but hackneys must be called to collect you. I'm sure there was a reason for the distinction at some point, but it remains.

A hackney cab is a type of taxi (one used in london), and can be hailed. A mini cab must be pre booked, like Uber or Addison Lee.

The distinction is usually to avoid lots of drivers milling about for riders and causing congestion for everybody else.