Is the shared medium an intrinsic side effect of a coaxial cable?
Couldn't you set up a twisted pair infrastructure to also be a shared medium?
It's theoretically possible but not really practical.
Could you set up a coaxial network not to be a shared medium?
You certainly could, but it would likely be a relatively expensive option.
Is it just a difference in logistic strategy?
Cable networks were primerally designed for broadcasting TV. Coax has the ability to support wide signal bandwidths and high signal powers making it suitable for broadcasting TV to lots of clients from one headend. It's relatively expensive though, so passive splitters close to the clients are the order of the day.
The phone network was/is a system designed for carrying phone calls. Twisted pair cable is relatively cheap allowing each client to be given their own pair back to the telephone exchange, however it has poor high-freqency/high power characteristics.
Neither network is ideal for carrying high-speed internet service, but few providers want to rip up their networks and start from scratch.
On the phone network side DSL uses has to use clever modulation tricks to correct for the crappiness of the cable and extend the usable bandwidth but the throughput is still poor, especially if the cable run is long.
On the cable network side you have a few challanges to data service. Firstly a significant portion of the available bandwidth is taken up by TV services. Secondly what is left for internet service is shared. Thirdly the splitters make the signal path very lossy, this is not so much of a problem in the downstream direction where you have a big amplifier at the transmitter and little interference at the receiver but is much more of a problem in the upstream direction where you have a small amplifier at the transmitter and lots of interference at the receiver.
Combining the crappy high-frequency behaviour of twisted pair cable with the splitting losses and shared nature of a cable TV like network layout would result in terrible performance.
Optical fiber offers both very high bandwidths and cheap cable. The downside is that it requires more expensive tooling and more careful handling. Optical is the obvious choice for newcomers to the market but existing providers with a large deployed base of copper and a large staff used to dealing with copper are more reluctant to switch.
Many existing providers have moved towards hybrid systems. Fiber is run to street cabinet and then VDSL or cable is run to the final customer site. Performance is improved over traditional systems because the length of the copper run is shortened and in the case of cable the level of sharing may also be reduced. This hybrid approach can deliver performance gains to an existing network at a lower initial cost than a complete move to fiber. However it means that active equipment must be maintained in the field.