I would also have thought that 'ABC Cabs' or whatever would insist that their phone number is on the side of all vehicles being driven in their name purely as a way of getting new business by the number sticking in people's consciousness. Many people (probably the majority in non-Uber areas) still phone for a taxi rather than using an app. Given this, branding is also beneficial in areas where there are multiple companies - otherwise how do I know which of a number of cars arriving at a station to meet the 18:08 arrival, for example, is the ABC Cabs that I ordered as opposed to XYZ Taxis ordered by someone else.
There are a couple of good points here. You mentioned 'ABC Cabs' - cab firms often named themselves as A1, or AAA taxis or whatever because they would be the first to appear in a classified directory (Yellow Pages/Thomson etc.) whenever anyone looked up 'taxis'. In many cases the phone number is the brand. The cab firm I worked for had acquired various smaller concerns over the years, to the extent that when someone called one number and was advised of no availability, quite often we'd get the same customer calling in on a different number (same booking system, same fleet) to be advised the same. One of our major competitors had 878787 as their number, but a smaller rival had adopted 878788 - presumably because someone somewhere who'd had a few jars might just mis-dial.
Because you've been given a description of it and its registration number, either by text or via the booking app if you used one?
Does any taxi business of any significant size (i.e. not "Bob's Cab" in the middle of nowhere) not do this yet? I'm amazed they are still in business if so.
It works because "if it ain't broke, don't fix it". While I'm all for technological solutions, and I'm sure that "Bob's Cab" in the middle of nowhere could benefit from this in some way, in most areas of the country people are still comfortable with dialing a number on their phone and hearing a human voice on the end of the line that will tell them that their cab will be approximately 10 minutes (or more likely on a Saturday night - "sorry, fully booked"). It's an instant response, and one that empowers the customer to decide "oh, I'll just wait", or "I'll try someone else". I worked for ComCab, which had a fairly large fleet in London and had adopted things like SMS notifications and IVR responses quite early on. While their system was
very slick in its operation (keystrokes built-in, no need for a mouse) - I, as a call-centre monkey had no way to view the bigger picture. We just kept on taking the bookings in, whether or not there was enough fleet on the ground to cover it. God forbid that it ever rained in London, because that meant that our breaks - in Aberdeen - were put on hold!
Let's not forget that most drivers are self-employed, and they pay a certain regular amount for their "radio hire" in order to receive work. They've probably paid to get their own taxi licences, and most will have paid for their own cars, but when it's chucking it down with rain and the taxi ranks are full, the "office" becomes redundant, and any driver with a "hackney" licence can book off and work the streets.