From someone who has worked from both sides as a dispatcher and a driver, I can tell you that there are still some solely radio car companies out there, the ones that I know will call "car x cleared x" to give the dispatcher an idea of which area they are in and then get told by a dispatcher whether to head back or stay put, the dispatcher will have written down, any jobs that drivers have pre allocated and most of these dispatchers don't do well when handed a computer and an app, these dispatchers have been at it for years and can run the office on their own better than any computer system can, on advantage of it is that drivers know that they have to call in when they pick up a flagged down hire and usually will tell the dispatcher where they are dropping off so giving the dispatcher an idea in their heads for follow on work. In terms of the computer based systems, there are cloud based ones and in the early days, you needed radio so that if the cloud system failed, or the boss had missed his monthly payment, you have a back up.
The bigger systems like Autocab, Auriga etc.. used to have hardwired dataheads, but again, you had the radio for backup as some of the older dataheads failed repeatedly (one car I know had 3 dataheads break on a Saturday afternoon, including one break in front of me with them not doing anything to it), even with a datahead, the systems would always have a REQ function where the driver would push it to get the dispatcher to call them over the radio, of course one major reason for the radio's not being redundant would be for the EMG function, at least if it was hit by accident, it would be rectified much quicker, one system that I had the pleasure of working with, when you pushed the emergency button, it asked you in big letters for your assailant to see that you had pushed said button and wanted you to push it again to confirm, not a good thing when you have someone trying to assault you, was part of a running joke in my office that as you were being assaulted you had to ask the guy hitting you to stop so you could push the button again to confirm you were being assaulted, the datahead systems were good too that as soon as you put on the meter, if you picked up off the street, it would automatically put you (P)assenger (On) (B)oard. The cloud apps were different, they would either require you to push a button on the app which is easily forgotten, or would automatically put you POB if you drove away from the address which is great if said address was plotted in the correct position in the software, if it wasn't plotted correctly you had a chance of getting a noshow as the same function also sent the text to the customer saying that you were outside, all these mistakes have to be watched by a dispatcher who could be dealing with phones and other issues.
One of the worst systems I used as dispatch and a driver was using mobile phones preloaded with said system, all is fine and dandy until most evenings when the signal would either drop as the system would only work on one network, losing you both way of comms and also jobs, or worst of all, go down completely on a Saturday night so nobody had any communication at all apart from the trusty radio with no tech services available, would show on another occasion a driver in the middle of the Caspian Sea while another was in Washington D.C when we were in Scotland.
The advantage of the older Datahead systems like autocab was though, that if you took care of the equipment, you could still use it 20 years later and if you didn't want all the latest features, not pay a penny, and you could still use the radio for booking return jobs via the driver etc... You had the best of both worlds.