I guess you can always think of a reason where a smartphone would be useful as in your example Vicki. In my experience of taxis, I find it reasonably straightforward to use my mobile from home to summons the taxi, they generally tell you how long they will be, you can even book one for a day or two in advance. Coming home I use my mobile phone to get my taxi.
I appreciate you cannot get a neat display of the location or ETA of the taxi using my 20th century method, but it works reasonably well.
A few years ago we went to see a recording of "Pointless" at Boreham Wood. We had to print out our email invitation and show it at the door to the studio. I think we were the only members of the audience to do this as most people had their invitations on their smartphones.
It's the same as ordering a takeaway from the local restaurant, most people appear to use an app on their smartphones for this, I pick up my mobile and order it as normal. No hassle and perfectly fine.
I think it's a question of what you have never had you do not miss.