Quick question...
Extend land-line (telephone lines) along all train railways and tramways. Put telephone booth into each train.
It's already progress, since currently, most mobile phones will not be able to make a call underground - and, for example, London underground can be very extensive.
Make sure that the booth accepts payments not only as cash-coins, but also from contact-less smartcard - it's much more comfortable than looking for coins of specific size and feeding them to the automaton.
Then, since you may need to send a fax or an SMS, instead of making a voice call - add more chips into the contact-less smart card (and appropriate technology into phone booth, so that it would be able to send the information given), so that it would have a simple, physical keyboard, a microSD card to store some information, such as owner's fingerprint (the automaton-booth would then compare visitor's fingerprint with visitor's card's information), and maybe, even all other fancy accessories: camera (if it is possible to make such a paper-thin camera), microphones, speakers, small high-resolution screen, GPS chip, accelerometer, barometer, gyroscope, magnetometer.
Only, no battery. The smart card would take energy from the booth-automaton, or from a separate stone-like portable energy source - battery, if you will. Going into hibernation when it has no energy. Using small included solar panel when it has to work without any external supply.
Make a phone like that, and see: will people use it? It will fit into wallet. It will not be turned on unless you require it to be turned on. It will be more secure, less distracting, more austere and business-like. There will be a wide range of options available, from the cheapest to the fanciest.
Just an insane idea. I am seriously worried about vulnerability of large sensitive touch-screens which are easily scratched. And it's obviously better for your mobile to be turned off most of the time, because it spends a lot of energy, and can be destroyed by water if it falls into a rain puddle. By the way, contact-less smart cards are already waterproof, aren't they?
Best wishes.
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Per aspera ad astra...