Agreed, for most services used in mobile networks today a NATed private IP address does the job. But there are some applications that require a reachable public IP address such as web servers, VPN gateways, chat servers, etc. Also agreed, these are mostly connected via fixed line connections but in some instances, e.g. for fallback solutions or in places where DSL links are not available, it's great for them to be reachable over a cellular network as well.
Unfortunately support of public IP addresses is seen as a niche service by most mobile network operators and hence they either don't support public IP addresses at all or only via obscure and unadvertised APNs. The more delighted I was when I saw that one of the mobile network operators in Austria is offering to use a public IP address for a connection via their web configuration interface with a simple on/off switch. Great, a mobile network operator who's willing to also cater for those with special applications!
And when thinking a bit more about it it's even more stunning in the light of many alternative fixed line network operators who are also not willing anymore to give out public IPv4 addresses, not even on request. Take a look guys, it can be THAT simple!!!
I recently signed a contract with an operator in Japan (Y! Mobile) and bought a cell phone from them (a Nexus 5). I was surprised when I saw on the documents the public IPv4 address associated to the device, clearly printed!