This has been talked about and proposed a number of times since the introduction of mobile phones. However with the introduction of the internet it was put off for some time. But as mobile calls and data become cheaper and as people become more reliant on their cellphone the choice to pay extra money to also have a fixed phone line will become unusual.
Telecom and Vodafone expect that the landlines will continue to exist in NZ for the next decade(1), however I believe that it will be pretty close to being obsolete by then. Several other countries are probably closer to doing this than we are. Once we get mobile plans in NZ where for the equivalent of 20Euro we can have unlimited phone calls, texts and data like in Ireland (2) () paying $99 for your phone line and broadband is going to seem like a silly idea.
Developing countries are often skipping the personal landline in favour of mobile devices too – these are much more adaptable and less infrastructure cost to set up (3).