All of this is also assuming that any organised crime are even using a Mobile Phone for sensitive communication, they could just as easily use an internet connection and tablet / laptop / computer encrypted on a public wifi connection, or as already mentioned above, wifi connected phone apps.
Of course you could introduce a system onto every public wifi access point whereby you needed to type in credit card details or even some kind of a National ID Card Number in order to Identify yourself to the wifi network and therefore make your use of it traceable, but I doubt that kind of system would sit well with those who walk down the street streaming seamlessly from every public wifi point available as any authentication and id verification process would no longer make it seamless!, plus many wouldn't like the idea of putting their personal details into what is a public internet connection in any case.
I suppose you could look to "Police" all roaming activity, in that you can't roam on another Countries' network until you have produced ID to that network, but that would require all Countries and all networks to have the same agreement, and can you imagine people on Holiday, arriving at say 6PM and not being able to use their phone via Roaming until they visited the nearest network outlet / phone shop to physically produce ID when it opened at 9AM the following day. Some people get great Angst if their network goes down for 15 minutes and they can't use their phone how would they go on for an entire day / night!. I can't imagine that would work well, or be workable for business travelers / lorry & bus drivers etc traveling through several Countries in a short space of time.
So where would you draw the line? given that there is more than one method of connecting a mobile phone to the outside world, and current roaming agreements would largely circumvent a Country based registration scheme.