What you suggest could be accomplished with mesh networking. GP is correct in saying the reasons are orthogonal to functional reasons. Phone systems have always been centralised like this. Billing is one aspect, but lawful surveillance is another.
With respect, if you think that mesh networking would have worked considering the scale and capacity needed, and relevant type of devices then I am afraid this is a case of not knowing what you don't know...
I was using Mesh networking as an example. Obviously it can’t handle heavy load or longer distances well, however it is much more efficient for local point to point.
If you like, you can consider just plain old VOIP where the central entity is used for discovery but the actual call may then be routed p2p though not in VoLTE and its successors of course because the media plane is also centrally routed.
They are not entirely orthogonal. You need a central base station with scheduling, high dynamic range and power control to maximize performance in an OFDM system. In addition, most cells used to use frequency division multiplexing meaning that the base station and phones send and receive on different frequencies. So lack of point to point capabilities can at least in part be explained by the design goal of optimizing for throughput and user density.
You do if you want to route across a broader area which is a different use case to what we are talking about. Two phones right next to each other are routes through the BTS even though they could easily route directly to one another and that is for non functional reasons.
No, they could literally not send on the frequencies they listen on in case of FDD. Enabling this would require extra radio hardware. Also there would need to be a some kind of encryption key exchange between devices which is not needed in the centralized setup. They could not easily route to one another without adding extra stuff.
